You live two lives. One is an ordinary, boring life that you don't mind the NSA finding out about. The other is as secretive as possible. No using credit cards. Nothing that requires ID. No flying, no buying alcohol.
One obvious problem with this is withdrawing cash. You have your public life, and the NSA sees you going to an ATM and grabbing $450, then it sees a transaction for $447 with an unknown person -- that's evidence linking your private identity to your public one. This is ameliorated if your public identity has a habit of withdrawing extra cash and a means of disposing of extra cash in a publicly acceptable way, like giving it to beggars, but it's still present. If your private identity has an income, though, and that income is sufficient for its expenses, then you can have wholly separate finances for both, which severs that link entirely.
A weaker link is one of location over time. Let's say the NSA can plot your public identity's location over time using things like bus pass usage, credit cards, phone calls, and security cameras with facial recognition, and they can plot your private identity's location over time using phone calls and security cameras. Eventually they'll realize that your private and public identities are occasionally colocated, or that whenever your public identity is in use your private has gone dark and vice versa.
Of course, that only matters if it's worse for you if the NSA has linked your public and private lives than if they merely have the ability to detain you during the course of your private affairs.