If there is an update available you can download it via the software updates menu (in settings > about). Occasionally I've known an update to be released only via the manufacturer's or carrier's website (in which case you'd download and install it via a computer), but this is unusual.
Otherwise, you would have to root the phone and install a custom ROM (software developed by an independent developer rather than the manufacturer), as long as one of these exists for your phone. Rooting is device-specific, so if this interests you please visit our main forum, and particularly the section for your device, to find out more about what is involved. Since I don't know what device you have, I cannot really say more.
I'm afraid that android does have to be built for the phone, so there is no generic version that you can install on any device, so your options are either to wait for an official update or find a custom ROM.