You may come to hate that pool. They're a LOT of work. What size is it? My former home had an above-ground 24 foot diameter pool with a deck built around 1/5 of it. It was a nice setup, but one that ultimately wasn't worth the hassle. I think it held something over 14,000 gallons. I think most residential pools are considerably smaller than that.
First of all--if it's under a tree or something, get rid of the tree. Constantly fishing leaves out of the pool sucks.
Second, since it's still early in the year, take pre-emptive measures all around the railings to prevent wasps from building nests (this is obviously a non-factor if it's an in ground pool). Wasps love building nexts up under the railings many larger above-ground pools have, and you will make them angry when you go swimming. Take it from someone who knows--clouds of angry wasps aren't much fun to share a pool with.
The water itself shouldn't be green--the green is most likely from algae growing on the pool liner. This happens when you don't treat the water for too long and don't have the filter system running. Let it go long enough and it will begin to look brown, and eventually black and stinking (yuck!). Don't drain it unless you like massive water bills (plus it'd take days or weeks for the typical garden hose to fill a pool). You'll need a special chemical called 'shock' initially to clear it up, and a test kit is a must. YOU MUST HAVE A WATER TEST KIT. Do your own water testing even if you end up paying for someone else to do the cleaning, because it's YOUR health on the line. Inadequately-treated water is bad, but so is over-treated water. You should probably have some sort of floatation device which you can put slow-dissolving treatment tablets in. You'll also need various chemicals (such as chlorine), a pool vacuum, and some sort of surface skimmer net. Hopefully the previous owners left you all these tools; if they didn't it can get sort of pricey.
You will need to periodically run the hose to add water to the pool. If you have to run the hose daily with nobody using the pool, that's a common indicator that your liner is torn and needs replacement. This requires you to drain the pool and should be done at the beginning of the year, so find out now if you need it. If the pool's sides are built out of aluminum, find out how old it is--old pools DO break (the 24-foot pool at my old place ruptured once, and required total replacement). If it's an in-ground pool, collapse is obviously a nonissue and it probably won't have a liner, either.
Your pool will have some sort of filter system. This system typically has a small skimmer attached to the pool to catch bugs and other floating stuff, a tank (typically filled with sand sold for this purpose) for actual filtration, and then a pump to return the water to the pool and create a constant current so the pool doesn't become stagnant and turn green. The skimmer and the water return hose might be built into the sides of the pool, or they might simply hang over the top of the rail. The types that hang over the top are easier to maintain. You'll need to get this running and operate it pretty much every day. You will have to clean out the filter in the skimmer regularly (usually daily). You also will likely need to backwash the system weekly or so, depending on how much dirt gets into the pool. The control to backwash is normally a valve attached to the filter. The motor for the pool's filter system also typically powers the vacuum when you clean your pool.
If you have kids, expect them to have green poop after they go swimming, so don't freak out if they do. Something with the chlorine causes it and kids seem to love drinking pool water.
Get your phone book and find a store in your area that specifically sells pool supplies. The guys who work in these places should be able to tell you exactly what you need. I haven't had to maintain a pool in more than ten years, and many of the parts were older than I am, so what I know may be outdated in some regards.
J_A_B
