1. THE INFINITIVE The infinitive is used: to say why you do something
I’ve just gone running to get some exercise.
He’s taken up tennis to make friends.
to say why something exists
There’s an example to help you.
after too and enough
It’s too cold to go swimming today.
He isn’t good enough to make the national team.

2. The infinitive is used after these verb patterns:
verb + to infinitive:
She agreed to meet him after work.
agree, appear, begin, bother, decide, demand, fail, hope, learn, manage, offer, plan, refuse, seem, be supposed, threaten
verb + (somebody) + to infinitive:
She expected to win the race.
I expect you to play in the match.
ask, choose, expect, help, intend, promise, want
verb + somebody/something + to infinitive:
The money enabled him to go to university.
advise, allow, enable, encourage, forbid, force, invite, order, permit, persuade, promise, recommend, refuse, remind, tell, threaten, warn

3. VERB + -ING The verb + -ing is used: after prepositions:
He’s made a lot of friends by joining the tennis club.
We watched a film about climbing in the mountains.
as subjects or objects of a sentence:
Climbing is safer than it looks.
He decided to take up adventure racing.

4. The verb + -ing is used after these verbs:
admit, appreciate, avoid, celebrate, consider, delay, deny, dislike, enjoy, finish, imagine, involve, keep, mind, miss, postpone, practice, regret, risk, stop, suggest
I really enjoyed winning that match.
She suggested playing a game of squash after school.
The verb + -ing is used after the following expressions:
it’s no good it’s not worth it’s no use it’s a waste of time
can’t stand can’t bear can’t help
It’s not worth joining that sports club.
It’s a waste of time entering the competition unless you’re really fit.
I can’t bear watching my team when they play badly.