On tour (granted the longest has been only 3 weeks) I
1) Wipe the chain (by backpedaling) to remove any larger debris.
2) Wipe off any buildup (dried lubricant mixed with dirt) from the cassette, chainrings, and derailleur pulleys.
3) Apply lubricant to each roller (use the lubricant you prefer, I use TriFlow).
4) Back pedal to work lubricant into space between pins/bushings/rollers.
5) Wipe off excess lubricant (by backpedaling)

I assume you could do a deep clean if you are taking rest days. In that case, removing the chain from the bike and placing it in a bottle (don't need to bring one from home, just use a large Gatorade or similar bottle) with some solvent probably isn't overkill. Even dish soap will work, though you may need to refresh several times, but it will get off the large majority of the grime. I think if you set the chain in the sun for an hour or so will drive off any water/solvent "trapped" in the spaces between the pins/bushings/rollers. Then put the chain back on and lube as usual.

Final word: as with all things touring, do what makes sense to you and that you are comfortable with.