7.62x54mmR is the old Russian military cartridge, used in the Moisin Nagant Model1891 rifles from the end of the 19th Century until the introduction of the 7.62x39 round in the 1940s, and still in use for some Russian machine guns. Old Moisins were imported to the US and were quite cheap and popular as hunting/target rifles. You can Google the Moisin of course, but bear in mind that the stocks may have been cut down from the military full stock for civilian hunting use. This will change the appearance of the rifle, and as the original was quite long, the barrel may have been shortened too, for practical hunting use, taking any bayonet lugs with it.
Check and see (without firing) if the bolt closes and locks comfortably on a chambered cartridge, and look for Russian markings on the rifle. Even if the alpha characters are in Cyrillic, there may be numeric characters which will give a clue. M1891, for example, or1891/30 (there was a major redesign in 1930). It should have an internal 5 round magazine - see if the rounds fit and cycle from mag to breech, extraction and ejection. Any difficulty may not necessarily mean that the rounds do not match the rifle, but if it is pretty old it may be that the cartridge headspace needs adjusting.
The round is rimmed, and there should be an annular step in the face of the breech where the rim sits. If using live rounds to do this, keep fingers away from trigger, and muzzle pointing in a safe direction. If you are not certain, then get a gunsmith to have a look.