These controllers are a dime a dozen to find.
http://tncscooters.com/index.php?route=product/category&path=41_74 They are often cheaper on ebay - eg search YK40-3 for example.
I would pick one that is rated to 20 amps - this will limit your power to about ~450watts so you don't cook your motor quickly.
As dogman says, two wires feed into the controller from the battery, and two wires supply the motor with increasing pulses of current to increase power (or the converse).
The other connections can usually be left alone. Unless the controller has a key switch facility - if so you can either use your existing one across those two wires, or short them out for testing.
If you get a cheap 3 wire throttle it makes connections easy. If you get a throttle with LED's to indicate power there will be a fourth wire - you can just leave that disconnected too. I don't like LED throttles as they don't tell you much. Use a 5 buck digital voltmeter when you get going.
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*If your Lead acids still work at all, why not just buy a controller and throttle and get the bike working. Then do the batteries.*
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Two bits advice on using lithium batteries. 1) Use a fuse - shorts on Lithium are super scary. 2) Be careful of low voltage cutout on the controller. If you use an 8s lithium pack (33.6v full, 29.7 volts empty) then your controller may cut out at say 31.5 volts. So you can only use half the capacity of the pack. Either use a 9s pack or bigger (may be a more expensive charger), or use a 24volt controller (as the amp rating is what mostly matters) and a voltmeter in line so you know how 'full your petrol tank' is. The latter is what I do.
Modded Aprilia Enjoy 'Race' & Enjoy 'City -10Y/o brushed Crankdrives.
Globe single spd aluminium with Q100 & 10s bottlebattery.
Dual 1900W BPM/Ezee gear hub for offroad.
900W Ezee Bakfiets / Cargotrike.
"Take the risk of thinking for yourself, much more happiness, truth, beauty, and wisdom will come to you that way." - Hitch.