What is the difference in participle gerund and infinitive?

Infinitives can be nouns, adjectives, or adverbs. Here it is a noun, the direct object of

"want": I want to buy a house. They look the same--to do, to act, to see, etc. You have to figure out whether it's doing the job of a noun, adjective, or adverb.

Participles are adjectives derived from verbs. In "a married woman,"married" is a past participle adjective that comes from the verb "to marry."

Present participles also can be adjectives: In "A swiftly moving river flows through town" "moving" is the participial adjective. It describes "river." The verb is "flows." Be sure to find the verb and distinguish it from an adjective.

Gerunds look like participles but do a different job grammatically. Here is "moving" as a gerund: Moving to a new town is difficult for children. Here "moving" is the subject of the sentence. A subject must be a noun. The gerund has a verbal meaning but is a noun. The verb is "is." "Moving is difficult." Gerunds can be direct objects or do any job a noun can do: I enjoy fishing. "Fishing" is the direct object of the verb "enjoy."

A prepositional phrase begins with a preposition and ends with a noun: "among my school books," for example, or "to the store." Be careful to determine which "to" you're dealing with. In "to the store," "to" is a preposition, but in "I"ve decided to major in astronomy," the "to" belongs with "to major," an infinitive.

Appositives rename nouns and are nouns themselves. Here is an example: My brother, a doctor, makes lots of money. The appositive is "a doctor."

There are no tricks. You have to analyze the sentence and figure out what each Word or phrase is doing.