How do you request a "pop up" IFR clearance?
Assuming you are not already talking to ATC:

You: Houston Center, Cessna 1234X, request*

Center: Cessna 34X, Houston Center, go ahead

You: Cessna 34X is a 172/U, 35 North IDU, 4500 ft, request IFR to Austin

Center: Cessna 34X ident, fly heading 270

Center: Cessna 34X is cleared to AUS via radar vectors, climb and maintain 6000 ft, squawk 5634

This is essentially the same as making a request for VFR flight following services with the exceptions:


Your aircraft needs to be legal for IFR.
You need to be rated and current for IFR.
You will receive a clearance.


If you already have flight following and need IFR, the controller has you on his scope and already has a strip for you, and you just need to ask him to make you IFR.  In that case he will just put you on an IFR altitude and give you a clearance limit and route.

*As noted in the comments, you may decorate this call with something identifying the nature of your request