I own a house with my sister. I would like to borrow against my half. How do I do that?

You can only borrow (or do anything) in agreement and signature with each other.

(You don't really own half the house, you own a half interest in the whole house. If you default on a loan, the lender can't chop half the house off.)

Unfortunately it doesn't work that way. How is the deed titled? Both names? How much equity. Who gets the property tax benefit? Who gets interest benefit?

It is theoretically possible for someone to loan you money secured by your half interest, but it would be foolish to do so, for any number of reasons. Therefore, from a practical matter, it isn't going to happen. You will need your sister to sign the mortgage, although she won't have to sign the note and would not be liable for a deficiency judgment, should you default.