How to increase graphic card memory.

Basically, what you have on the card is what you are stuck with.

It has been years since graphics card manufacturers have included memory expansion sockets for adding more memory. Everything is now SMT (google it).

You need specialized training and equipment to do this. A $10 Rat Shack soldering iron will not work.

Then you need to find the memory chips.
 
OK. I went looking. The base technology is about 4 years old. It's an interesting approach to the problem, costs a little speed, but looks like it may make some games playable on budget cards. Do the newer cards support it?

I doubt if that's really what the OP had in mind, but it is a solution.