Ok Silent One's post was pretty much accurate about size, however, there are always exceptions. You can setup a 10 gallon salt water tank successfully but it's going to be more difficult to do right than a fresh water tank. I've been through fresh and salt water tanks for years so I have a pretty good idea of what would work and what doesn't.
There are different levels of salt water tanks, from beginner to advanced and the costs involved will also rise with the level of complexity of the tank and inhabitants.
These are may classifications for beginner to advanced tanks.
1. Beginner - fish only tank with only a few hardy fish
2. Intermediate - fish and live rock
3. Advanced - fish, live coral, live rock, live sand, invertebrates, etc.
With the beginner you'll only need to monitor water quality as temperature is automatically controlled. Basically partial weekly or biweekly water changes and monthly filter checks. For a 10 gallon tank you should only house 3 small fish less than 1" and don't overfeed. When mixing your saltwater you should use filtered water not tap water preferrably using a Reverse Osmosis system. You also need your tank to go through the nitrogen cycle so that you have enough bacteria in the filter for biological filtration. You should get an external biowheel filter and preferably a protein skimmer. It you're going to do it right even at the beginning level, you'll still need the equipment I mentioned. The most difficult thing about maintaining a tank is disease control.
Personally I really got tired of the high maintenance of salt water aquariums so I'm back to fresh water. My freshwater tank is only 5 gallons and contain only guppies. They're very colorful guppies though and I have live green plants so it looks very nice in a fresh water way.
These are the essential things you'll need for a salt water tank. You do not need an air pump.
1. Biological filter - I recommend the Penguin Bio-Wheel Mini wet/dry filter for your size tank $13
2. Heater 50 Watts - Acura, Visi-Therm, Ebo Jäger, or Tronic $15
3. Thermometer - You need it to adjust the heater - Sticker type $2
4. Hydrometer for testing salinity - I recommend the floating glass hydrometer type as it's fast needing only a quick glance and accurate too - $17
5. Protein Skimmer - I recommend the SeaClone or Prizm because it's cheap and includes the water pump - $70
6. Water test kit
7. Salt mix
Now all you need is the sand/gravel, sterilized rock/ornaments, fish and tank which should come with a light fixture. Try to get one with a flouresent tube not the halogen type. Total cost should be around $150 for a 10 gallon salt water beginner tank.
I recommend this site for more information on supplies or care.
http://www.drsfostersmith.com/
These are the kind of freshwater fish I have. As you can see they're very coloful.
http://www.liveaquaria.com/product/scateg.cfm?siteid=21&pCatId=1100