Hi Mike!
The first job is to make your tank fit for fish. You need to read the pinned topics about cycling your tank.
Basically, every tank needs a colony of bacteria big enough to process the ammonia excreted by the fish. Some of these bacteria are naturally present in the tap water, but not enough to deal with the concentrations of a fish tank. But they will multiply if they are fed.
There are two ways of achieving this:
you can either start with a very few hardy starter fish. This is the oldfashioned method. The disadvantage is, that however hardy, these fish are for the first month or so living in a bath of toxic chemicals. You can alleviate their situation by testing the water daily and doing a partial water change whenever the ammonia or nitrites rise. Then after all traces of these chemicals have finally disappeared, you can add a few more fish, and so on until your tank is fully stocked
or, you can do a so-called fishless cycle. In this you simulate the above situation by adding drops of ammonia (as described in pinned topic), and you don't put any fish in until this process is completed, that is until you have seen first the ammonia, then the nitrites spike and then go down, leaving a hefty legacy of nitrates in the tank. You then do a big water change to dilute the nitrates and then you're ready to add fish
Just letting the tank sit, or adding bacteria out of bottles (unless it is the product known as Biospira or Bactinett) is not going to get the bacteria growing; they need food.
But in your case, I agree with previous posters that you need to know why you have already got ammonia in your tank. Have you tested the tap water?
Then for hardy fish. By hardy fish, one usually means fish that can withstand ordinary water parameters (ie do not have very specific requirements as to ph and hardness) and that can even cope with small amounts of ammonia on a temporary basis. This is not to say that hardy fish have no specific requirements at all, or that you don't have to know anything about them. All fish have their own specific needs that must be taken into accounts. Some of them just happen to be easier to cater for in a home situation.
The fish usually mentioned as hardy beginners fish are danios, black widow tetras and platies. Of these, both danios and black widows are unsuitable for a 10 gallon tank: they are schooling fish (need to be in groups of at least 6-8) and very active, so need quite a lot of swimming space.
Platies can cope with a 10 gallon tank, as long as the water is not very soft and acid (if someone has problems keeping both mollies and platies alive, this might be the reason). So they should be fine. All you need to consider here is sex ratios. They can be kept in mixed gender groups- then you need to have at least 2-3 females per male (the males are sex machines and won't leave a single female alone). And you will get fry (though the parents may eat them). If you want to avoid fry, you can keep males only, but then you need a group of at least 5 to spread aggression- which will take up all the space in your tank. Almost the easiest option is to keep females on their own. You may still get fry, they are often pregnant from the shop, but eventually the supply will dry out.
Other options, if you have done a fishless cycle might include:
corydoras- scavenging bottom feeders, who need to be in groups of at least 3, great fun to watch, need sand or smooth pea-shaped gravel which has to be kept clean (gravel vac at least once a week)
White Cloud Mountain minnows- coldwater fish, so you need to keep temperatures down, but a school of these would look good
glowlight tetras
honey gouramis are sometimes hardier than dwarfs. I appreciate that there may be hardy individual dwarf gouramis out there, and somebody may well have struck lucky, but given the general look of the ones I have seen around the shops for the last year, I would say that statistically speaking you are likely to end up with a sickly individual. If you go for honeys, make sure you only get one male- gouramis are territorial
a Siamese fighter (betta) and then later on when the tank is mature you can add some tetras
I am sure there are other tetras that would suit but can't think of any just at the moment