The process that I'll describe will take a bit of your time, some good gun cleaning solvent (I recommend Hoppe's #9), a good brass/bronze brush of the appropriate size*, a cleaning rod, some good cotton patches, a warm work area that's protected from solvent and mess, and some elbow grease.
Remove the barrel from the receiver.
Install a cylinder or improved cylinder** choke tube.
Soak your brush with solvent and “scrub” the barrel from the chamber to the muzzle end for several minutes. I recommend no less than 4-5 minutes. Really scrub it and use plenty of solvent. DO NOT SWAB IT OR DRY IT.
After your scrub (for at least 4-5 minutes, longer is better – don't cheat on the time) let the barrel set wet, don't swab it, for at least 15-20 minutes at room temperature.
Scrub your barrel again with your brush for a few minutes, you may use more solvent to help “wash” your barrel while you're doing this.
Now, it's time to use the cotton patches. Swab your barrel until at least 1 comes out clean and dry. Remove the choke tube you installed and clean the area that it occupied with a toothbrush or brass brush for this purpose. Don't use the brass brush you used for cleaning the barrel. Wipe it dry with a lint free cloth and then lightly oil the area. Always keep some type of choke in your barrel to prevent foreign material from fouling the threads.
Look at your barrel. It should be shiny and bright.
(If it has pitting, gouges, machine marks, etc. it may never pattern as well as you'd like and you may want to have it professionally polished. Be aware that may cost $100.00 or more. You and only you can decide if a better pattern is worth the additional cost.)
Reassemble your gun.
If you're ready to pattern test it now, leave the bore dry and install your turkey choke. If you plan to store it, you may want to put a protective coat of lubricant on the exterior and interior of the barrel. Be certain to remove all lubricant prior to shooting.
This process involves some work but it will pay dividends in most cases by helping to increase the quality of your patterns.
Lastly, be certain to dispose of all solvent soaked rags, newspapers, etc. in a responsible and safe manner. Some products are flammable and must be treated as such. Disposal may require some extraordinary caution. Some solvent products are harmful if used in an unventilated area. Please read and follow all label directions and cautions on containers.
*835/935 use a 10 Gauge Brush - not 12 Gauge
**This is done to make it easier to clean the barrel. It is sometimes difficult run a cleaning rod, brush or patches through tight turkey chokes. Ported chokes can be hard on brass brushes and sometimes "eat" cleaning patches. You should clean your turkey choke with at least as much care as you clean your barrel.