Try Remington Arms website. Or you might want to try eBay, they have reproductions of the original manuals on occasion. Keyword, Remington Model 513T or 513S (the sporter version with same internals).
Go to Remington's website. There you can download a copy of the owner's manual. (did that for my 870)
Start with a cleaning rod, patches, powder solvent, oil, and a copy of the owner's manual. If you do not HAVE the owner's manual, go to the website for Remington Customer Service, and download the manual. Before starting to clean, be certain that the shotgun is UNLOADED.
If you go to Remington's web site, you can request one or download one.
You can download an owner's manual for fee at Remington's web site.
You can request one for free from Remington at http://www.remington.com/library/downloads/owners_manuals.asp
Buy a service manual
That's still available from Remington, you probably have to register on line and request an obsolete manual. http://www.remington.com/library/downloads/owners_manuals.asp
You can download an owner's manual for free at Remington's web site.
You cannot download the service manual for a 2005 Pontiac Sunfire for free. You will need to call the manufacturer and purchase a new manual.
You can order one for about $16 or download a free manual. See the links.
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You contact Remington customer service, and ask for an owner's manual for your rifle. Then read and follow the manual.