Any mob trap within 16 blocks of the bottom of the map will catch slimes as well, but you have to be careful to not hurt the slimes too much to get them to split the most. Punching and drowning are the safest ways to ensure that they'll split into more slimes. Also, you want a large room so that bigger slimes will spawn which can then have more splits.
The most important thing besides the depth is that it's in a chunk suitable for slimes. Slimes can only spawn in 10% of the chunks, picked randomly depending on the seed. You can calculate which chunks are suitable with this tool by trunkz though: http://www.minecraftforum.net/topic/397835-find-slime-spawning-chunks/
They only spawn a tenth as often as other mobs, but they'll also spawn in any light level, so if you're digging for diamonds at bedrock level, you'll usually find quite a few naturally.
A water block becomes a source block when there's at least 2 other source blocks next to it (not counting diagonally). You start with the very edge and place two water blocks like so. This will give you a 2×2 square of water sources.
__________
|Wo |
|oW |
| |
| |
| |
W = water source placed by you
o = water source generated by the water mechanics
Now, simply scoop up any source block (it will refill), and dump it diagonally from the outermost block.
__________
|Woo |
|oWo |
|ooW |
| |
| |
Repeat until you hit an edge. Which source block you take doesn't matter, they are all infinite (as in, will refill instantly) at this point.
__________
|Woooo |
|oWooo |
|ooWoo |
|oooWo |
|ooooW |
As you can see, to fill an n-long square, you need n bucket loads (actually, only 2, since after that, you can refill from the pool).
To fill the entire rectangle, dump a bucket every other row on one side. The very edge block always has to be filled.
__________
|Wooooooo|
|oWoooooo|
|ooWooooo|
|oooWoooo|
|ooooWWoW|
So to fill an n×m block rectangle, you need n + ceil((m - n) / 2) water sources, with m being the longer side. Again, only 2 if you're talking resources, because after that, you're drawing from an infinite pool.
Here's a video of a guy using this technique on a square:
(Note that he always refills from the still source blocks for some reason, but as noted above, any source block will do.)
Best Answer
As the Tekkit pack doesn't seem to include Mekanism and its generators (if I'm not mistaken), Thermal Expansion appears to be the best way.
What worked for me best and what was the easiest way to move my quarry after use was to use Tesseracts and Electrical Engines. While Electrical Engines have a bit of a conversion loss, they still work quite efficiently. Use however many Engines you can power and push that energy directly into the tesseract, and set the tesseract directly next to the quarry.
If there is a more resource efficient way, I don't know it.
Edit: As Tekkit-Lite doesn't seem to have the Electrical Engines, you can use an "Energy Link", which might even be more efficient. It should be in the PowerConverters Mod that's included in Lite, try to look that up here. I do not know if that takes up more energy than the opposing side needs, but I doubt it. However, a Quarry uses really a lot of energy, so sometimes it might seem like it needs too much. You should just test it out, maybe with an EU reader or something similar.