The instructions in any manual for rifle reloading will apply with several caveats.
The bore and groove diameter can vary tremendously in old milsurps. They can range from nearly .308" to at least .317". Slugging your bore is one way to check (pound a lead ball down the barrel with a dowel or brass rod) and it's best to use a micrometer, not a caliper, as you want to get as close as possible. If it's a 5-groove barrel it's problematic to measure. A second way is just to try bullets of different diameter and see which ones shoot best and if any of them tumble. .303B bullets are available in .3105", .311", and .312". I have a Martini-Enfield that slugs .3165" but will still shoot .312" decently well. I used to have a No.1 Mk.3 that slugged .315" and it also shot .312" decently. In both rifles, .3105" bullets tumble and keyhole quite often (but not every shot). I have a 2-groove No.4 Mk.1 now that mics .313" but it'll eat anything (I guess the lack of rifling causes more material to swage down into the two grooves that are there).
If you're shooting cast bullets it's a whole other matter. If that's the case you really want the bullets to be .001" to .002" oversized. Personally I cast .311", .314", and .317" for various .303B rifles. If you don't cast yourself, and you have an oversized bore, good luck.
Case head separation is another problem with many milsurp .303B's. The heads of the cases stretch backwards if you try to headspace them off of the rim. In nearly all rifles, even the worst ones for headspace problems, the first round is unlikely to cause the case head to come off so it was good enough for the military who had no interest in reloading cases. Neck sizing only, or FL sizing but adjusting the die so it just kisses the top of the shoulder, are the two normal ways to extend case life. This allows the cases to, in essence, headspace off of the shoulder which will put the case head against the bolt face instead of having it floating in the air inside the chamber.
I don't like going to the range without a broken case extractor in .303B if I'm shooting any reloads. Even if I checked the cases and they don't appear to have case head stretching problems, they can still pop off sometimes. A broken case extractor will save your shooting session from ending early. I got mine for under $20 and I've had to use it a half dozen times in the past few years. When a case head separates you will get a little puff of gas in your face (always wear safety glasses while shooting) and you may have a sooted up chamber.
I'm sure BigEdP51 will be here soon to drop his wisdom and very helpful pictures related to .303B reloading.
The only downside to .303 in a SMLE type rifle is the locking lugs a the rear of the bolt allow for a minute amount of bolt flex. The brass can stretch and separate 1/2 inch from the rim after only 1 or two reloadings. The large military chambers don't help either.
Neck sizing will help a small amount but you will still get head separation.
If you have a rifle that locks up front it is pretty straight forward.
The rear locking bolt isn't the main part of the problem. The oversized military chambers is what causes most of the problem. One of the worst .303B rifles I had for case head separation was a P14 which is in essence a Mauser action. The shoulder of the chamber was so far forward the cases could practically rattle around inside if they were FL resized.
I have some RP brass that I bought new, used the o-ring trick on to fire form, and usually just neck size but sometimes when they get stiff I'll use a FL sizing die but only ever kiss the shoulder. They are up to 6-7 firings and none of them have had a separation yet. If you setup the brass to headspace off the shoulder instead of the rim, they will last as long as any other average brass. I also anneal every 4-5 firings to avoid split necks.