To supplement the good advice Todd Shell gave -
You say you know they were not installed correctly - what specifically makes you say that ? You also did not say what type of material the frames are, and what style of window (double hung, casement, slider, etc). Also - are the leaks on both fixed and opening units, or only opening type windows. If only opening type likely to be the seals on the moving units, if fixed units too then likely to be a caulk problem.
If it is coming in around the glass at the glass-frame interface, then cleaning off the outside joint (see a web video onhow to do this - it is not tough) with a razor blade scraper or single-edge razor blade and recaulking to seal the glass-wood (or glass-metal or glass-vinyl) interface should handle it.
If it is coming in around the outside of the outer window frame or leaking into the house from under the trim around the inside of the window, then if you are ladder handy climb up and take a good look all around the outside of the window frames. If not ladder handy you might be able to duct tape a hand mirror to a stick and lean out the window and move it around outside an open window to look at the caulk joints. At 10 years if they used a cheap latex caulk or window putty originally, it could be your caulk is deteriorated and all you need to do is cut/peel away the old caulk seal from around the outside of the window frame and recaulk with a 30-year silicone or latex-modified silicone caulk (they come in several colors). Recaulking would not correct a lack of proper flashing installation (which should have stopped this type of leakage from outside the window outside frame) but as long as the frame and caulk are intact, that does not matter - the flashing is only a backup in case water gets through the caulk, to prevent the water from getting into the wall - not the primary water infiltration barrier. A carpenter, handyman, or window repair or installation shop can handle recaulking.
If you have casement style windows (the moveable windows open horizontally, swinging open out from the house face), then it is possible the face seals are going bad - open the window and check all around to see if the seals (usually white flexible plastic bulbs or strips embedded in grooves cut into the window frame) are intact and not smashed down flat. These seals are replaceable - by some window repair shops and lumber yards, from millwork shops carrying that make of window, from the manufacturer, and commonly at Home Depot or Lowes. These can be replaced by you if you are handy, otherwise by a window repair shop or millwork door and window shop.
If it is coming in at the gap between slider units (2 sideways sliding units per window) or double hung (one unit slides vertically past the other unit) windows, then the window fit might have loosed up with seasonal wetting and drying, or the seal strip between the window units is shot. A window repair company or sometimes a finish carpenter can fix this, as can a millwork shop that does on-site repairs. This assumes the problem is new, not a continuing one since you bought the house. If a problem since you bought the house, also check that the window units are installed right one out - on sliders, the one that overlaps on the outside of the other should be on the side blowing rain comes from (for instance, on a south-facing wall, if the storm winds commonly come from the east when it rains, then the east sliding unit should overlap over the outside frame of the west one). That keeps driving rain from impinging directly on the seal between the two units which, because it has to slide past the other, cannot be made truly watertight. For double hung units, the top unit should be in the outside track so water running off it drips free off the bottom of the frame, rather than pooling on top of the bottom unit frame and running into the house.
If you are having water on the inside bottom of the window in the winter only, be sure it is actually a leak - could it be winter condensation running down the glass (or freezing at the bottom of the window panes and then melting), then running off onto the frame, causing rot and mold ? If this is the case, the most seere damage will be on the frame around the glass, not the outside frame. In this case, your problem is moisture and window temperature control, not a window leak. See more detail in my response to another person with similar issue here - http://answers.angieslist.com/Who-rep...
Think these over, and as Todd said, if you think it is coming around the outside of the frame, you could open up and look through the interior drywall for interior wall leakage damage - water staining, mildew, wet insulation, etc. Before opening up drywall, I would first suggest you carefully pry off the trim around the worst window (if you are careful not to bend it too much, you should be able to reuse it - is usually just nailed with 3-4 relatively small finish-type nails per strip, that will just pull through the strip as you pry it off). Using a strong light, this should show you if the water is coming in around the outside of the frame or not - if at the top most likely from outside caulk or drip edge failure, along sides likely top or side caulk failure, or below the bottom ONLY then most likely leakage from rain hitting the lower frame or window sill outside, and leaking in through the frame joints near the bottom of the window (which can be sealed or caulked EXCEPT where the window makes direct contact); or from water running off the bottom of the window sill and wicking back under the window. There should be a small groove or step-up cut on the underside of the outside sill near the front edge to force the runoff to drip off rather than wick back under into the wall, but not all windows have this. Without it, water can wick (by surface tension) all the way back up under the window sill and into the wall. If this is happening, would be water staining on the underside of the sill and probably onthe wall right under the sill.
A good test, assuming your window and perimeter caulk looks good so you think the problem is in the glass frame seals, is to have one person watch inside while someone else goes outside in the dark with a very strong flashlight (like a 6V cell lantern) with a rag wrapped around the head (so it seals against the window frame to restrict the light to just the place being checked) and run it all around the window frame, sliding unit edges, and junction between slider units to see where the light comes through readily. Anyplace light comes through is a place water can come through.
Another test is to take a hose, and while one person stands inside and watches, carefully direct a low-pressure flow against different parts of the window till you see leakage. Work from bottom to top of the window, and do not do this for more than a minute or so or until you see water coming through, because if you have a significant leak then you are putting more water into your walls.
Good luck, and if you want more advice after checking out possible sources, post back here as an answer to this same thread.