Depends on where you get stuff at, I would steer clear of craigslist, I've seen a few good deals but many more overpriced crappy setups. Local fish stores are usually way expensive on dry goods as well.

Basic setup
10 gallon tank = $20-$25
Powerhead = $20
Salt = $45 for 150-200 gallon mix, will last you a long time
Heater = $20
Sand=$15-20 for a 20 pound bag, depends on how deep you want your sandbed, I run mine pretty shallow


Live Rock = $2.5-$15 a pound, best bet is buying online or from someone breaking down a tank, look for nice shapes, coraline algea is good, but no hair or bubble algea, you will want 10-20 pounds

Lighting = depends on what you want to keep, most people keep nanos for coral since they are too small for the majority of fish, at least you want power compacts, t5s or a 70-150 watt metal halide would be better, anywhere from $100-$350, bulbs are expensive as well and need yearly replacement

You won't need a filter, the live rock and sand will do that, I just do water changes on my nanos, you might want a small powerfilter to run carbon or filter floss though. It is expensive starting out, there are lots of different all in one nano setups as well, red sea max, nanocube, aquapod, biocube, etc if you want a cleaner looking setup. I've ran a 2.5 gallon, 5.5 gallon, 10 gallon, 12 gallon Aquapod and now have a 24 gallon nanocube with the back part ripped off and 150 watt Sunpod for lighting. I don't even want to know how deep I am for cost.