Use "would + like" to make polite requests or to ask a question in a polite way. The contracted form of would is 'd. When speaking, you'll usually use the contracted forms (I'd, you'd, he'd, we'd) instead of the full forms (I would, you would, he would, we would).

Requests:
▶ I'd like another cup of coffee, please.
▶ I'd like another few days to finish the proposal.
▶ We'd like another bottle of wine.
▶ We'd like a room with a view.

Polite questions:
▶ Would you* like some more coffee? (You could also say, "Do you want some more coffee?" but using "would" makes the question more polite).
▶ Would you like to stay for dinner? (You could also say, "Do you want to stay for dinner?" but again, using "would" makes it more polite).
▶ Would you like some help with your luggage?

* Note that "would you" is often pronounced as one word: wouldja.

Ask "wouldn't you like" if you want a positive response:
▶ Wouldn't you like to stay for dinner? (This sounds more like you really do want someone to stay rather than just asking, "Would you like to stay for dinner?").
▶ Wouldn't you like another cookie? (You're encouraging the person to go ahead and take another one).