First of all, it is important to state that a verbal is a verb form which acts as a noun or an adjective. There are three types of verbals: Participles (past participles and present participles), Gerunds and Infinitives.
- Could you help me find my running shoes?
- "running" is a participle functioning as an adjective since it is modifying the noun "shoes".
- We were hoping to begin a game of chess.
- "to begin" is an infinitive functioning as a noun (to identify its function, you may ask the question: What were you hoping?, and the answer is "to begin a game of chess")
- I would rather be sleeping!
- "sleeping" is a gerund functioning as a noun. Although gerunds look like present participles (because they end with -ing), a gerund is a noun not an adjective.