"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:
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.