For example can you install a pair of 1 GB RAM chips with a pair of 256 MB chips? And what if they are different brands?

Theoretically there should be no issues but ideally it's best that you don't. Also, if you mix RAM chips you will not get them to run in Dual / Triple Channel mode.

They should work, but if the 256 one is slower (mhz) than the 1gb one then it's best not to use it.
example:
1gb 800 mhz cl6 + 256mb 667mhz cl7 = 1.25 gb 667mhz cl7
which by my opinion will perform worse than a 1gb 800mhz cl6

If both have the same speed (mhz) or the small one is faster than use them together, if not then it's best to keep it simple and only use the 1gb one

edit: the old one is also very likely to have errors and some computers give out compatibility problems even if it worked in the beginning.

I would just suggest getting another 1G of the same type, usually you can get RAM fairly cheap. Just be careful about buying used RAM.

I read on Ask Leo's site that it varies from computer to computer, and you have to check with the manufacturer. On some computers you can't mix chips, on others you can mix as long as you have pairs next to each other, on others you can mix as long as you stagger the pairs.

On Crucial.com they give you the details for any specific computer.

I am using two different brands of ram 3x2GB sticks ...... two of them are of one brand and 1 is another;but same timings/speed etc. I have no issue; however, i was forced into this situation due to availability issues of my older dd2 sticks. Therefore, given a chance I would prefer to have them all from same manufacturer/type.