Looking to replace the alternator belt on my 2000 mitsu mirage.....there is no belt on the alternator, guess i lost it somehere on the way home, car ran for a bit, then conked out.....any advice or tips on replacing it?

I would replace the steering pump belt at the same time you do the alternator belt (buy both).
To take off the alternator belt . First , take off the negative battery cable so you do not blow an expensive fuse on the positive battery cable clamp(or a block fuse under the hood). Facing the back of the car , reach UNDER the alternator and loosen the bolt on the bottom right side, now loosen the bolt on the adjuster block on top, you can now turn the adjuster bolt and move the alternator to change the belt.
To take off the steering pump belt on the front of the motor, you need to loosen the nut on the back side of the pulley it holds the adjuster pulley in place . With the adjuster pulley loose , you can use the adjuster bolt to move the pulley to adjust/take off the steering pump belt.