We can sometimes use for + ing to talk about the purpose of a thing. When we do, it means the same as to + infinitive.
  • What is that for? It is for opening envelopes
  • This bell is for calling the waiter.
  • This bell is to call the waiter.

When we talk about the purpose of somebody's actions, we cannot use for + ing.
  • I went there to ask for help.
  • You will have to queue a long time. to get tickets.

However, it is sometimes possible to use for + noun for this.
  • I went there for help.
  • You will have to queue a long timefor tickets.

We can also use for + object + infinitive to talk about a purpose.
  • I gave her a notebook for her to write down new English words she found.
  • They sent a form for me to sign.

We also use the pattern for + object + infinitive in sentences after is or was.
  • The plan is for us to get to Barcelona by lunchtime.
  • The objective was for them to get the work finished by the end of last month.

We can add details to a noun by using the pattern for + object + infinitive
  • That is an expensive place for them to stay.
  • There is a lot of work for us to do.
  • There is no need for you to be so aggressive.

We also use the pattern for + object + infinitive after certain verbs and adjectives.
  • I am waiting for him to make the first move.
  • I have arranged for you to see the bank manager tomorrow morning.
  • We are keen for you to take the job.
  • I think it would be good for you to take a break now.