Would

In past:
I think I will be late to the party.

I thought I would be late to the party.

For unreal situation:
If I were you, I would run away.

If I had known, I would helped you.

If I won the prize, I would travel the world.

For request:
Would you mind carrying this bag?

Would you mind giving your pen?

Offer & invitation:

Would you like to have some coffee?

Would you like to come with us?

Wish: (I would - I'd)
I'd like to go home now.

I'd like to have some coffee.

Preference:
I'd rather take that dress.

I'd rather go home.

in my opinion:
I'd say, this dress suit you well.

I'm not a doctor, but I'd say he needs some medical attention.