If the rim is off the bike you will need to set up some sort of a truing stand. Can be the axle in a vice. If you go the HF route beware the rod and cones that come with the stand are junk. You can get a ground 12mm (I think) rod from a machine supply place and have cones made. The HF rod/cones are not precise so the cone will sit off center to the rod which induces a large error out at the rim.
Mark the rim where the weld is. It helps to have some colored tape for marking where adjustment is needed. As others have said take penetrating oil and put a drop at each spoke/nipple. If any of the spoke threads are really rusted I would replace the spoke and nipple.
Ignore the weld point for now unless you have wobble/hop more than 1 spoke to either side of the weld.
I do wobble first. The biggest mistake you can make is to start tweaking spokes without giving thought to what you are doing and the reaction it will have on the wheel. THINK ABOUT WHAT YOUR DOING! Mark your biggest sideways movement. You will want to pull the rim away from this spot. If the wobble is abrupt, (withing 3 spokes) and not large give the widest point a 1/4 turn to tighten. Each side of this spoke on the same side give them 1/8 turn. If the wobble is long, (4-5 or more spokes in duration) give the widest point 1/2 turn and then 1/4 turn to either side of the widest point, then 1/8 turn to the next spoke out from the widest point. You will need to loosen spokes on the opposite side if you turn more than a 1/4 turn.
For run out, It is similar to the above but instead of tightening on one side of the rim you tighten on both the left and right and loosen spokes 180 degrees opposite the tightened spot. You again work out from the highest point to spokes to either side of the high point tightening/loosening as needed.
Now go back and check the wobble and adjust and then check run out. Keep doing this until the rim is true. You will also want to check for offset of the rim to the hub. A front wheel off a K1-K6 750 will have an offset to the left (rim left of hub as sitting on the bike) You want the center point the hub (between the spoke attachment flange is) to be in line with the center of the rim. To shift the rim over it is the same as wobble except you do all the spokes on one side (tighten) and loosen on the other.
After you mount the tire and inflate it you need to go through the above and make sure the rim is true. If you want to balance the wheel you will need a truing stand. You need almost zero friction at the axle to do this and the axle/bearings/seals have too much friction.
Work slowly and THINK about what you are doing. It takes patience but is straight forward. If you go to a shop to have this done expect to pay through the nose and don't expect to have a good job done and you need to check their work. Few shops these days have kids that can do this properly. Lacing/truing a wheel is a dying art like buggy whips were 100 years ago.
-P.
