Upgrading the memory in your Mac (known as RAM) is a drastic solution — especially if you have a MacBook Air — but it's worth considering if you want to seriously reanimate your machine.
Various guides can be found — both on and off Apple's websites — to upgrade the RAM in whatever Mac you own and, while expensive, it can give a computer a whole new lease of life.
Caveats do apply: RAM is expensive — especially when bought from Apple — and buying the wrong type (desktop instead of laptop, for example) can break your Mac. Upgrading the RAM in newer MacBooks is also very tricky if you don't have the right tools (although iFixit do provide stellar guides).
Trying the other points in this guide may be as well before replacing RAM.