1) What are the components on it, specifically the shifters? They'll probably be Shimano, but who knows. [Pre-reply edit, looks like Suntour...]

2) When you move the right shift lever (for the rear gears), does it click/notch? If so, that means it is indexed, which it most likely is as Techniums were made in the indexing era.

3) How many cogs (or gears) are there in the back/on the rear hub?

4) What is the biggest cog (in number of teeth) in that cluster of gears? That will help determine if we need a normal rear derailleur with a short cage (short distance between the two pulley wheels). If the count is 28 teeth or less, than a short cage rear derailleur is sufficient.

As always, pictures (of the bike, shifters, and rear derailleur primarily) help us immensely. Giving us numbers also helps immensely. We should be able to sort this out quickly.