Phrasal Verbs consist of a verb plus a particle:
verb + adverb or verb + preposition or verb + adverb + preposition.
The meaning of this combination is mostly very different from the verb and the adverb or preposition alone.
There are no rules that might explain how phrasal verbs are formed correctly - all you can do is look them up in a dictionary and study their meanings.
In fact many phrasal verbs are metaphorical, and if you understand the metaphors they use, it will be easier to understand and remember their meanings.
Phrasal verbs are mainly used in spoken English and informal texts.
Many phrasal verbs are transitive, meaning that they take an object. Other phrasal verbs can stand alone (intransitive verbs).
Some phrasal verbs are separable (the verb and the preposition can be separated, putting the object in the middle), while others are inseparable (the object must come at the end because the verb and the preposition must stay together).
Separable verb:
Correct: Put on your coat.
Correct: Put your coat on.
Inseparable verb:
Correct: Get on a bus
Incorrect: Get a bus on

How to remember English phrasal verbs?

The first thing to do with phrasal verbs is to learn them as phrases and not only as separate words. Try to remember them as if they were a single verb.
The second thing that will help you is to remember them in groups.
For example, make a list of phrasal verbs with the word get in them and try to remember them.

You will find it easier, if you put them in groups of verbs with the same preposition. For example, phrasal verbs including the word ON. It is useful to group them on the basis of their meaning and using.
The third thing that will help you learn phrasal verbs is to make up or write sentences that will help you remember how they are used.
The fourth important thing about phrasal verbs is to remember if there are any other prepositions which always follow them.
For example: "I get ON well WITH my sister."

Groups of Phrasal verbs with the preposition ON:

MOVEMENT/POSITION (opposite of OFF = on a surface of something, covering, touching, attached to, refer to a place)
Cling on - Hold tight. He clung on to power for another ten years.
Close on - Get nearer, almost. I think there are close on three million unemployed at present.
Follow on - Leave to meet someone after they have left the place you're at. The summit is a follow-on to last year’s Economic Conference.
Get on - Enter a bus, train, plane, etc. We got on the train at Birmingham and went up to London.
(Note: get IN A CAR and GET OUT A CAR)
Have on - Be wearing/Have an electronic device switched on/Have an arrangement.
Kate had her new dress on.
Leave on - Not turn off. Don’t leave a computer on
Log on - Begin to use a computer system, as by entering a password. Have you already logged on?
Put on - Start wearing/ Deceive, lie. Kate put on her coat and went out.
Slip on - Put clothes on quickly. Kate slipped the jacket on to see what it looked like.
Take on - Allow passengers on a ship or plane/Employ.
We’re not taking on any new staff at the moment.
Try on - Put clothes on to see if they fit . Why don’t you try that dress on?
Turn on - Start a machine/Attack/Cause someone to feel attraction or pleasure. Is your computer turned on?
Switch on - To make a machine or piece of equipment work. Don’t switch on the light.

CONTINUING (used for saying that someone is continuing to do something)

Continue:

Carry on - Please carry on with your report. If you carry on spending money like that, you’ll end up in debt
Get on - Stop complaining about the work and get on with it. 
Can we please get on, because there are a lot of things still to discuss.
Go on - The speech went on for almost an hour.
Keep on - I was getting increasingly tired, but I kept on working.
Press on - The government is pressing ahead with its plans.

If somebody talks continuously we can use:

Bang on - Talk at great length. My parents are always banging on about how much better life was 50 years ago.
Drone on - Talk boringly for a long time. He was droning on and on about his ordeal.
Go on - Talk continuously. The speech seemed to go on forever.
Ramble on - Talk at length without getting to the point. 
Quit rambling on - I’m tired of listening to you.

Crack on - Continue doing something with energy. We had to crack on to get everything finished on time.
Drag on - Be unnecessarily long. The talks dragged on for months.
Dwell on - Spend a lot of time on something. He tends to dwell on the negative aspects of his performance.
Play on - Continue playing a sport though there might be a reason to stop/Continue playing music.
We played on in spite of the rain.
Run on - Continue for longer than expected or planned. The speech ran on for hours.
Stay on - Remain longer than anticipated. Kate promised to stay on for six months.
Walk on - Continue walking. She walked on without a backward glance.
Wave on - Make a hand signal to tell someone to keep moving. The accident was bad, but the police waved us on.

PROGRESSING (movement forwards, advance towards completion, maturity, or perfection)
Act on - To take action because of something like information received. The police refused to act on his complaint.
Add on - Include in a calculation. Let's add on to this.
Be on - Be functioning (of machines)/Take place. The news won't be on tonight.
Bring on - Cause something to happen or speed up the process/Make something appear. Her new piano teacher has really brought her on.

Get on - Make progress, deal with something with a reasonable degree of success. How did you get on in your exam?
Go on – Progress. She went on to become a MP.
Grow on - Like something that you didn't like at first/Become gradually more evident. I don't think much of your new record, but I suppose it will grow on me.
Move on - Change the subject or your job/ Make people move from a place. Now, I will move on to a new question.
Spur on - Encourage someone to continue. The thought of the bonus spurred her on to complete the work on time.
Tack on - Add something that wasn't planned. At the last minute they tacked on a couple of extra visits to my schedule.
Work on - Improve or develop. You need to work on your handwriting.


BEGINNING (a start, the point in time or space at which something starts)
Call on - Ask for help/ Visit/Challenge/Ask someone to do something, especially to speak in public. We could call on my parents if we have time.
Cheer on – Encourage. I’ll be there to cheer you on when the race starts.
Chew on - Thinks about something carefully before deciding. The investors have several economic reports to chew on.
Come on – Encouragement/Start an illness/Start functioning (machines, etc).
I saw a light come on in an upstairs window.
Cotton on = begin to understand. I didn’t cotton to him at first.
Egg on – Encourage. Don't egg him on!
Embark on - Start a project or venture. When will you embark on your new project?
Figure on – Plan/expect. I hadn’t figured on him reacting this way.
Go on – Happen/Start doing or taking something/Start working (electric/electronic equipment). I really must go on a diet!
Sign on - Agree to participate/Employ. We’ve signed on three new members of staff.
Start on - Begin to use or consume. I'm just about to start on the cleaning.


DEPENDENCE
Bank on - Count or rely on. Kate might arrive on time, but I wouldn’t bank on it.
Bargain on - Expect something to happen (usually negative). We hadn't bargained on such a long wait.
Depend on - To rely on something or someone, especially for support or maintenance. Children depend on adults for food and shelter.
Get on - Have a good relationship. Kate and Helen don’t get on.
Bear on - Influence, affect/Be connected or relevant to something. Do you have any information bearing on his disappearance?
Count on - Depend, rely/Expect something to happen and base plans on it. You may be disappointed if you count on getting that loan.
Hinge on - Depend very much or completely/Be an essential point for the development of a story. A lot hinges on the result of tomorrow’s match.
Reckon on - Expect something to happen and plan for it.
Kate hadn’t reckoned on having twins!
Rely on - Depend on someone or something; to trust in someone or something. Elderly parents often depend on their adult children.


THOUGHTS and FEELINGS
Dawn on - Finally realise or understand something. I was about to pay for the shopping when it suddenly dawned on me that I'd left my wallet at home.
Decide on - Choose, select. I've decided on blue for the bathroom.
Lead on - Falsely or cruelly raise hopes. She led him on about her desire to get married.
Sleep on - Think about something. Let me sleep on it and give you an answer tomorrow.
Weigh on - Make someone worried. He's under huge pressure at work and it's really weighing on him.

BEHAVOIUR (Used to describe a behaviour, either positive or (more often) negative)
Be down on - Have negative feelings toward someone. It's not fair of the boss to be so down on a new employee.
Grass on - Report someone to a person in authority.
Dan grassed on them to the local police.
Jump on – Criticize, attack. The students jumped on the college president after he spoke.
Lean on - Put pressure on someone to get them to do what you want. The Prime Minister’s been leaning heavily on him to resign.
Leap on - Show interest in or try to use something to your advantage. She found herself leaping on the suggestion.
Let on - Tell a secret. He knows more than he lets on.
Pick on - Bother, annoy, criticize or make fun of someone. Why do you always pick on me?
Pin on - Attach the blame to someone. They can’t pin anything on to him.
Rat on - Inform authorities about someone's wrongdoings. He ratted on me, and I got in trouble.
Set on – Attack. The lions set on the zebras.
Tell on someone - Report someone to an authority.
If you don’t stop hitting, I’m going to tell on you.
Urge on – Encourage/Persuade or pressure to accept something. He urged restraint on them.

 

OTHER USEFUL PHRASAL VERBS WITH ON
Cut back on - Reduce expenditure. The government has decided to cut back on spending on the armed forces.
Draw on - Exploit or use knowledge, skills or information for a specific purpose or aim. His novels draw heavily on his childhood.
Lay on - Organise, supply. They laid on a beautiful buffet lunch.
Live on - Use money for basic necessities. We can hardly live on £500 a week.
Quit on - Stop working, associating or being friends with someone, especially when they need support/Stop working or functioning. The car's battery quit on us when we were a mile from the city.
Save on - Reduce or avoid consumption to cut costs. It was a warm winter, so we saved on electricity.
Sell on - Convince someone/Buy something then sell it to someone else.
Mary sold me on ordering pizza for dinner.
Settle on – Agree. The two sides have not yet settled on a price.
Wait on - Serve people in a restaurant/Provide someone with everything they need or want/Wait for a result before being able to make a decision. The manager waited on a customer.