"I'd like to..." is an abbreviation of "I would like to..." Use this phrase to ask for services at stores, banks, and so on:

Hi. I'd like to deposit this into checking, please.

I'd like to send this via registered mail.

I'd like to cancel my membership.

You can also use it in an email to someone when you're in a position of authority, like when you're acting as a customer.

It's also possible to write "I'd like to ___" in emails to your boss, if you're doing something that's normal and expected. For example, if you have a specific number of vacation days that you can use, and you're allowed to use them whenever you want, you can write:

I'd like to take off the week of April 3rd.