I'm not sure if I should do this but I'm trying to meet a game's minimum requirements. If I should do this, how do I do it? I have an AMD Sapphire 7770 and an Intel Core i5 3470 3.2 GHZ if that matters.
Your question is confusing. Are you meaning the RAM on your motherboard or the VRAM on the GPU? If the latter then you can't unless you by a card with more.
If you're speaking of shared video memory, that's changed in your BIOS. Navigate through there and look for something along the lines of "dedicated video memory" or "shared video memory".
That's really your only option. Any else would require buying a new GPU.
Your 7770 is a dedicated card that is better than your integrated 2500 series on the CPU. You can't dedicate more memory to the card. You would have to buy a new card with more ram.
I'm not sure if I should do this but I'm trying to meet a game's minimum requirements. If I should do this, how do I do it? I have an AMD Sapphire 7770 and an Intel Core i5 3470 3.2 GHZ if that matters.
Dedicated VRAM is VRAM that comes with the card and is used exclusively by the GPU and no-one else, it is based on a different technology than the DDR RAMs the system use.
Dedicating more RAM to the graphics (only integrated graphics works this way) is actually exactly how 'Shared video memory' works, the system diverts its RAM to the integrated graphics usage.
VRAM requirement on games is not a hard number you have to follow for the game to work (it is not like Hard disk space requirement), but a general rule of thumb stating what kind of GPU you should have. EG if the game has minimum requirement of 1GB VRAM, it is recommending that you have a GPU with at least 1GB VRAM, not actually have 1GB RAM dedicated to video processing.