If there are two verbs after each other, the second verb is either the gerund (which is the ing-form) or the infinitive.

She wants to help us.	the infinitive
We enjoy sailing.	the gerund

There are no rules as to when to use which. There are verbs after which we use the infinitive, there are verbs after which we use the gerund.

afford	We can't afford to buy a new car now.
agree	Bob agreed to take the kids to shcool.
arrange	We didn't arrange to meet, we met by chance.
decide	I decided to learn English very well.
deserve	This threat deserves to be taken seriously.
fail	Frank failed to understand the problem.
forget	I forgot to send you the e-mail.
help	Drink this whisky. It'll help to forget that jerk.
hope	Do you still hope to win the race.
learn	Sam is ten years old, yet he hasn't learnt to say hello.
manage	They managed to catch the 6.20 train.
need	We need to talk.
offer	He offered to help us.
plan	They planned to move to the country.
promise	She promised to call me back.
refuse	Randy refused to lend money to us.
try	I tried to lift the suitcase.
want	I wanted to help them.

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admit	Paul admitted stealing the money.
avoid	I avoid meeting my boss.
can't help	I can't help sneezing. I have a flu.
can't stand	She can't stand waiting. She's very impatient.
deny	Zoe denied knowing about the plan.
enjoy	I enjoy swimming.
fancy	Do you fancy going to the cinema?
finish	They've finished painting the house.
give up	I'd like to, but I can't give up eating sweets.
imagine	I can't imagine giving a speech to a lot of people.
mind	I don't mind working in an office all day.
postpone	We can't postpone cleaning these rooms any longer.
practise	You must practise writing more.
risk	I don't want to risk losing my job.
spend	My son spent the whole weekend watching TV.
stop	My wife will never stop complaining.
report	Lots of people reported seeing the flying saucer.
waste	You're just wasting your time reading this.

After prepositional verbs, we have to use the gerund, too. This is a rule.

think of	I'm thinking of changing my job.
admit to	Todd admitted to stealing the money.
result in	He was late again, which resulted in losing his job.
look forward to	I look forward to hearing from you.
come round to	I'll never come round to answering my e-mails.
succeeded in	I've succeeded in persuading him to come.
object to	I object to your smoking.
prevent from	I'll prevent Joe from selling his house.
insist on	She insisted on finishing the job that day.

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There are some verbs that can be followed by both the infinitive and the gerund, and there is no significant difference in meaning.

love	I love skiing / to ski.
like	Do you like reading / to read?
hate	I hate waiting / to wait.
start	The child started crying / to cry.
begin	We begin walking / to walk.

After the verbs love, like, hate the gerund is more natural if we speak generally. If we are more specific, we can use the infinitive.

I love driving.	- general
I love to drive when there's little traffic.	- specific

After like, we can use the infitive if like does not mean enjoy.

I like to wash up the dishes immediately after dinner.	- We don't enjoy this, do we?
I like to get my teeth checked by a dentist every now and then.	- It's not enjoyable, either.

In the case of would like, would love and would hate, however, we can use only the infinitive.

I would like to help you, but I can't.

Would you like to read this book?

We would love to go to your party.

I would hate to work here.

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There are a few verbs that are followed by an object and then a bare infinitive, an infinitive without to.

let sb do sg	I never let the kids eat sweets before lunch.
make sb do sg	Todd made us do the job again.
help sb (to) do sg	He helped me (to) understand the problem.