Is this a hypothetical question, or did you strike gold?
If you hit a stash of ancient coins or your shovel pulls up pottery shards, put your shovel down, cover the area with a tarp or plastic, and secure the edges so no cats or snoopy neighbors can burrow under. Then throw back a shot or two of very strong alcohol to console yourself and call +7 (916) 146 5327, the hotline of the Moscow cultural legacy department, which is manned 24 hours a day, seven days a week. Someone will come out to examine the site, which must be left untouched to help specialists learn as much as possible about what was there, how it got there, how long it was there, and so on. They will then take over the recovery of the artifacts. If it's on your property, throw back another shot and hope or pray that they won't want to dig up your entire yard or house to find more treasure.
So if it's on your property, do you get to keep it? Or get a finder's fee? Or at least get one measly coin? No, no, and no again. The law says that all archeological finds belong to the state. So if you catch sight of a glint of gold in the pile of dirt dug up on the street near your Moscow apartment building, you can grab it — but you have to hand it over, even if the workers had tossed it away.
What you do get: the thanks of a grateful nation for helping them enrich their knowledge and understanding of the past.
Now don't you feel better?