Finite clauses must contain a verb which shows tense. They can be main clauses or subordinate clauses:
Is it raining? (main: present)
I spoke to Joanne last night. (main: past)
We didn’t get any food because we didn’t have enough time. (main: past; subordinate: past)
Non-finite clauses contain a verb which does not show tense. We usually use non-finite verbs only in subordinate clauses. We usually understand the time referred to from the context of the main clause. We often use a non-finite clause when the subject is the same as the subject in the main clause:
I had something to eat before leaving. (I had something to eat before I left.)
After having spent six hours at the hospital, they eventually came home.
Helped by local volunteers, staff at the museum have spent many years sorting and cataloguing more than 100,000 photographs.
He left the party and went home, not having anyone to talk to.
The person to ask about going to New Zealand is Beck.
You have to look at the picture really carefully in order to see all the detail.
After, although, though, and if
We often use non-finite clauses after some subordinating conjunctions like after, although, though and if:
By the end of the day, although exhausted, Mark did not feel quite as tired as he had in the past. (although he was exhausted)
The proposal, if accepted by Parliament, will mean fundamental changes to the education system.