Well, that's a very nice looking 1898.  You have the 1896 rear sight which is most likely what it had originally.  It looks like it might have been plated and polished for ceremonial duty... perhaps with a VFW or American Legion.  How's the bore? 

To clean it, just do like you would any other rifle.  I always remove the bolt and clean from the receiver end with a long rod (prevents undue muzzle wear).  I use Hoppe #9 and a bronze brush to scrub, then swab and oil with Remington oil.  To remove the bolt, lift up on the extractor while turning the bolt to the left and back.  Install in reverse order.  Further disassembly is not difficult... but you must NEVER try to snap off the handguard.  Remove the barreled action from the stock, and remove the rear sight.  Then, SLIDE the handguard off the barrel.  Assemble in reverse.  Removal of the loading gate and such is not normally necessary for cleaning unless you have a problem.  I perform a full disassembly about once a year to check things out, clean and lube.  Otherwise, I usually just clean the bore and action.

I shoot my Krag every month in Vintage Rifle Matches.  Yours could be a great candidate for that also!