Hi. Don't feel badly. You're trying to do the best you can by your pet, and that's all you can do. Asking for advice is the first step! A filter is very important. Try to get one rated for 2x the amount of water she is swimming in. Turtles are messy! You can also do weekly partial water changes. About 25% of the water.
Yes, you need a UVB bulb, the turtle uses it to create vitamin D3 and absorb calcium. As for a basking area, it needs to be completely dry, so she can get completely dry. Try using something cheap like egg crate (some stores call it light defuser) and make your own with some zip ties. It also needs to be warm, about 88-92 degrees Fahrenheit (or so I've read). Just make sure she can't get out!
The tank needs to be deep enough for her to swim and use all her muscles, so twice the length of her shell in water depth. And about 4x the length in, well, length. An easy way to do this is a storage tub (like Runnermaid) of a kiddie swimming pool. The water should be treated with a to remove chlorine and heavy metals. You can find cheap bottles of solutions used for this in the fish area of most pet stores. The water should be 76-77 degrees.
As for food, as babies they need mostly protein, but when they get older they need their diet to be 75% plant matter and the other 25% protein. Zoomed makes a good low protein food for adults. The best greens to feed, that can be fed every day are red leaf lettuce, dandelion greens, and turnip greens. All of these greens can be found at the grocery store in the fresh foods area. Sliders can also eat certain water plants if you can get your hands on some. I hope that helps! And, great job on trying to take care of your pet. You're headed the right way.
With man, some things are possible. With God, all things are possible.
1 RES, Jade.
1 calico cat, Sassy.
1 black lab/springer spaniel/akita, Razzle.
1 Beta, Quill.