Question

How can you tell what kind of infinitive is:
-a noun
-an adjective
-or a verb?

Answer 1

Infinitives are verb forms. They can act in the place of nouns sometimes, but they are primarily verbs.

to go
to walk
to be
to think
to be able
to judge
to write
to read
to understand
etc.

Answer 2

The infinitive can also act as adjectives, example. the ability to run fast, "to run" describes what ability.

It can also be an adverb. The boy swam the river to save the dog. "to save" tells why he swam.

Check this site.
http://owl.english.purdue.edu/owl/resource/627/03/
http://www.chompchomp.com/terms/infinitive.htm