Use would like for a thing you want. It is a polite way to say it. (I'd like = I would like.)
I'd like a thing
I'd like a coffee, please.
She'd like two tickets.
We'd like a table for four.
Try it: ___ a coffee, please. (I'd like / I'd like to / I would to like) Answer: I'd like — Coffee is a thing, so use I'd like and then the thing. You add to only before an action, not before a thing.
I'd like to do something
For an action you want to do, use would like to before the base verb. Don't forget the to.
I'd like to order now.
She'd like to speak to you.
They'd like to book a room.
Not "I'd like order now." — say "I'd like to order now.". Before an action, you need to: I'd like to order.
Try it: ___ now. (I'd like to order / I'd like order / I'd to like order) Answer: I'd like to order — "Order" is an action, so you need to before it: I'd like to order. And to never goes between would and like.
Try it: ___ book a room for two nights. (I'd like to / I'd like / I'd to like) Answer: I'd like to — "Book" is an action, so you need to: I'd like to book. Use I'd like (no to) only before a thing.
Offering: Would you like...?
To offer something politely, put would first: Would you like...?
Would you like a coffee?
Would you like to sit down?
What would you like?
Try it: ___ a coffee? (Would you like / You would like / Do you would like) Answer: Would you like — To offer, would comes first: Would you like a coffee? You don't add "do" before would.
No, thank you.
To say no to an offer, say No, thank you. or No, thanks. It is short and polite.
Would you like some tea? → No, thank you.
Would you like a bag? → No, thanks.
Would you like to sit down? → No, thank you. I'm fine.
Not "Would you like some tea? → I wouldn't like tea." — say "Would you like some tea? → No, thank you.". To say no to an offer, use No, thank you. "I wouldn't like" sounds strange here.
Try it: Hiroshi: Would you like some cake? Sofia: ___ I'm full. Choose Sofia's answer. (No, thank you. / No, I wouldn't like. / No, I don't like.) Answer: No, thank you. — To say no to an offer, say No, thank you. "I wouldn't like" and "I don't like" need a thing after them, and they are not how people say no to an offer.
Try it: ___ a cup of tea. (I'd like / Would I like / I'd like to) Answer: I'd like — A cup of tea is a thing you want, so use I'd like and then the thing. ("Would I like" asks a question; to is only for an action.)