48,000 miles is kinda young to have transmission problems.Any possibility there's still factory or an extended warranty on the car?
Properly flushing a transmission involves two steps flushing all the fluid out, then replacing the old filter with a new one (simply replacing the filter will replace only about 25-50% of the fluid).:
(usually they use a machine that includes both a reservoir for new fluid and a tank for old fluid...but if you are cleaver (and careful) you can do it without making a mess yourself.
You will need perhaps 2 cases (24 cans) of fluid. Because you will be replacing more than all the fluid in the trans, including the torque converter (which usually is not drained when one simply replaces the filter). You will also need a new filter for that transmission (best to verify the transmission model, perhaps it is stamped in the trans oil pan under the car, because the same model car could have several transmission options and it is not fun to have the thing torn down and then find you have the wrong part.)
At the radiator there are two lines from the trans. (usually the bottom tank or the RH tank on a cross flow car) In case of the cross flow car, I think the top connection is old fluid from the box to the rad and the lower one is back to the box. You should check this to be sure!!!) You will need to disconnect the "to the radiator" connection and rig a hose-deal to pipe it to a large bucket or small garbage can. Then you'll need to rig a 1-2 gallon reservoir you can fill as you go, with a hose connecting to the return line. the reservoir should be several feet higher than the line for gravity flow.
Then you idle the engine. the old fluid is pumped into your catch container and new fluid is sucked back in from your reservoir. You are done with Part One when the stuff coming out is as clean looking as the stuff going in. Reconnect the lines as they originally were.
Then, for a complete job, on to part 2. This is replacing the filter...which is in the transmission oil pan. You don't want to do this before the flush because then you'll be pushing all the old fluid thru the new filter. You will have to drop the pan (they usually do not have drains, so you loosen the screws and let one edge hang much lower and the stuff in the pan will spill out. You will need a 2+ gallon catch basin (I have used a large restaurant "bus tray" available at Sam's Club pretty cheaply). Yes, this will dump out about 3-5 quarts of the new fluid you just put in. When the stuff quits running down your sleeve remove the pan and pull out the filter. Replace the filter, replace the pan gasket (if it has one, or use silicone seal as instructed in the instructions that should be in the filter box). Then top up the trans and you are done.
Most of us will then have to spend an hour or so cleaning up the mess we just made in the street or driveway, but I imagine you are far smarter than us and won't have made this mess.
Or you will take it to a transmission place and have it done.<G> The transmission place may even have an adjustment they can make.
When I used to work in an oil change place we charged about $175 for this. However I would not recommend taking it to anyplace other than a dealer or transmission specialist (the guy who did ours managed to do it wrong every now and then and several expensive transmissions got fried and the boss got 6o buy new tramissions for them. (why did he do it wrong, lack of proper training. That's why I recommend a transmission shop or Ford dealer.