The following is for working rifles only; rifles that only see a box of work a year from a clean bench need not receive this much treatment. Adjust schedule frequency upward according to your environment if you have a lot of blowing dust or other harsh conditions...like if you often find yourself swimming with your rifle.
Weekly:
Remove bolt from rifle, use compressed air to blow off all grit and grime you can, wipedown all exterior surfaces with a clean rag. Lightly oil or wax bolt surfaces to prevent rust, and after inspecting the rear locking surfaces for any sign of galling, relubricate with GREASE the BACK of the locking lugs (front doesn't need lube, and only acts as a dirt magnet), the cocking cam, maybe a touch on the extraction cam surface. Basically, as stated above. Set aside.
Use the best tools you have to clean out the action of the rifle and remove all the grit and residue you can, including the chamber...may as well do this at the same time. Clean the action BEFORE you insert a boreguide to clean the bore, because a good tight-fitting bore guide will shove all the grungy grease and oil to the front of the action into the bolt recess where it is much harder to get out. If you have a locking lug and recess cleaning tool set, now is the time to use it; if you don't have one, get one.
Last: flush out the trigger group from above with butane lighter fluid. Hardware store.
Biannually or annually:
Do all of the above first, but do not relube the bolt. Then, dissassemble the bolt down to the individual firing pin, mainspring, shroud level. You will need tools for this, if you don't have them already. Clean, inspect, and lightly lightly reoil (with a rust preventative) every component, and reassemble. Wrap a single or double loop of PTFE pipe-thread tape around the shroud's threads before reinstalling in the bolt.
If applicable, punch out the ejector retaining pin and remove the ejector and spring. Use compressed air and/or sovent to clean out the recess. Clean, inspect, reoil, and reinstall the ejector. If you have a fixed pin ejector, good for you...you have a better system, and it doesn't need cleaning or lubing.
If you have a stock Remington, do not mess with the extractor (obviously, since it is staked in!). If you have Sako or M16 extract, feel free to remove if you please, and clean and relube with oil. If you have a Winchester/Mauser or similar claw assembly, remove, clean, oil, and reinstall.
After complete bolt reassembly, repeat all weekly/monthly critical lube points and action cleaning as above.
Every barrel replacement or 2: (assuming ~10,000 total cycles including dryfiring.)
Replace mainspring in action. Gre-tan.
Store your rifle with the bolt decocked.
-Nate