Slide squeezing vice jaws used to be available from Brownells, but I haven't looked to see if theyre still there? If you have a set of precision rail plates to peen against, the rails generally spread more than enough to let you file and lap them to fit the ways in the slide side-to-side.
If you do have to squeeze the rails to get contact, you generally do this in a large vice which has an integral anvil. After you tighten the vice on the squeeze jaws, you strike the anvil with a deadblow hammer to stress-relieve the slide and minimize its tendency to spring back. A bloody nuisance and I've only ever had to do it once.
It should be noted that the old G.I. slides on the 1911 were soft slides. It was found they tended to peen into a jamb at the slide stop, so later they began heat treating slides and spot heat treating the slide stop notch harder than the rest of the slide. This all adds up to a modern slide being more springy and harder to squeeze than the early ones were. I suspect this fitting technique was pioneered on the old guns where it was easier to do.
I'll disagree with some of the comment here that implies barrel fitting is a substitute for slide fitting. Barrel fitting is much more significant, but, in general, if you want the best accuracy you do both. A general rule of thumb the late Col. George Nonte cited is that accuracy depends about 50/50 on mechanical accuracy and practical accuracy. Mechanical accuracy is what makes a gun accurate in a mechine rest. Practical accuracy is what makes it user friendly; sights, trigger job, ergonomic grips, etc.). There isnt much point in making a mechanically accurate gun if you are going to leave a gravelly seven pound trigger and tiny military A1 sights on it.
Of the mechanical 50% of accuracy, bushing fit accounts for about 15%, slide fitting maybe 5-10%, while getting the barrel to lockup right is the remaining 25-30%. There are exceptions: individual guns where the importance of one of these elements may be exaggerated or lost because of something peculiar about that particular gun, but these are fair general guestimates.
One other reason for proper slide fit is to minimize how high locking lugs have to go up to lock the barrel firmly into battery. I've seen guns where the slide is loose enough vertically that a fit barrel, after cutting the link lugs, required such a long link that the assembled gun couldn't cycle. The back of the link lugs had to be filed forward before the barrel would fully unlock and lie down in the frame cradle (bed) in counter-battery. Needless to say, the barrel feed ramp then overhangs the frame feed ramp and has to be filed forward more than usual. This weakens support for the case. Lowering the rails to keep the slide down minimizes these problems.
Another reason to fit the slide is that some guns are loose enough that they don't always cycle in a straight line. A not uncommon problem is the bottom of the recoil spring housing in the slide rubbing the frame dust cover, but not consistently. You see marks on the slide if this is happening. The irregularity can affects target accuracy and, with a marginal load, can affect functional reliability. A gun that locks up the same way every time tends to feed more reliably than those which do not because the fitted slide moves along the same path every time.
You always get some grumbling that a tightly fit gun can't reliably cycle when full of mud and sand, as the 1911's original looser tolerances allowed. The counter argument is that unless you are planning to fight World War I over again, being prepared for trench warfare has less value than achieving improved reliability under more contemporary circumstances.
Nick