If it's just mild surface rust then you could try steel wool. Use the finest grade you can find, though if it's chrome you'll find it's remarkably scratch resistant.
I've read that copper or aluminium wool is better ideally, as it doesn't leave behind any residue that can rust away in nooks & crannies on the frame.
You'll know whether your frame/part is worth this extra precaution.
Oxalic acid is good for treating more serious cases of rust, handy for removing inaccessible rust inside the tubes, there are threads here on its use. Can eat the metal as well as the rust though if you leave an item submerged too long. It should be neutralised afterwards.
I use Hammerite Gel Rust remover for any deep rust, but it can be expensive if you need to use a lot of it. If it's bare metal rather than chrome you need to seal the metal with paint/lacquer/wax pretty quickly afterwards or the rust will soon return.
