Webs,
Unless you can get the full friction pulloff procedure for the application, in your case, the lathe spindle, then you need to use a rule of thumb.
That is, tighten up the nuts until there is no end play at all, but also no drag on the bearing, then give the nut about another 1/16th of a tightening turn.
Normally you should check the rotational friction pulloff by using an arm and spring balance on the chuck, but as long as the threads on the spindle end are fairly fine, what I have suggested using the rule of thumb should be OK.
This operation preloads the bearing.
The machine should be run for at least a couple of minutes, or even longer, before being used or for any long period of inactivity during the day. This ensures that the spindle has expanded to it's working length (normally, it is about 0.002" that the spindle 'grows' in length, due to heat produced).
If you don't do the preload or the warm up procedure, then the spindle can in fact become loose endways, or you will get bad finishes due to the bearings brinelling before the spindle growth has had time to relieve the preload pressure.
If leaving the machine for extended periods of inactivity, say for the winter period, the preload should be released, otherwise the bearings can become permanently brinelled (rough running) and require replacement.
Ideally the bearing should be oil lubricated, but in your situation, that isn't possible, but as suggested, a good quality bearing grease can be used. But only fill the bearing a max of 50% full, otherwise hydraulicing between the bearing parts can cause early failure.
This has all been discussed at length in previous posts.
Just a little note about bearings in lathe heads. You will invariably get much better surface finishes with a lathe that has correctly adjusted plain bearings, either Babbit, cast iron or bronze.
The reason for fitting raced bearings is to allow the lathe to turn at higher rotational speeds, but you do lose out on the quality of the finish due to the inherent 'ratcheting' of a ball or taper bearing.
That is why a lot of people still swear by using old iron with plain bearings, and they don't mind about the higher speeds that raced bearings allow. I have never had the superb finishes I used to obtain since I swapped over the plain bearing head to a tapered bearing one on my Atlas lathe, and now the new lathe, again with bearings in it.
John