Most importantly, an infinitive is a verb with the word "to" in front of it.
The infinitive is used as either a noun, adjective, or adverb. The role an infinitive plays in the sentence may be either the subject, direct object, predicate noun, adjective, or adverb in a sentence.
Examples:
Subject: To walk seemed foolish when we had a car.
Direct Object: We all wanted to sleep.
Predicate Noun: His goal is to finish the race.
Adjective: She lacked the humor to laugh.
Adverb: Susan read to learn.
As you can see, infinitives may be anywhere in the sentence, but they are identifiable because of the word "to" in front of the verb.
Remember not to split infinitives: do not put words between "to" and the verb. NOT I like to slowly walk home. BUT I like to walk slowly home.