All you need is an image manipulation program so that you can edit the texture sheet. Paint.net is a possible choice for this, but you could also use Photoshop or GIMP, or any other program that gets the job done.
In case you need to know how to get to the texture file you change to make the pack:
Click the start button and type "%appdata%" without the quotes and press enter. That will open up your appdata folder. From there open the ".minecraft" folder, then the "bin" folder.
The next part is kind of tricky. There is a file in the bin folder called "minecraft", which is a .jar file. You have to open this like it's a .zip folder. You may need to open it with WinRAR (another program, you can google search it).
When you open the minecraft.jar file as a zip file, you will see some folders and a ton of CLASS files. Scroll through those files, somewhere down the long list you will find a .png file called "terrain". Extract that to your desktop, or any folder you want, and that is what you will open with the image editing program and modify to your liking.
Once you're done changing the textures, save the file with the same name ("terrain") in a folder wherever you want. The folder's name will be what your texture pack is called. Then you need to make that folder into a .zip file. If you got WinRAR for the last step, you can do this by right-clicking on the folder and clicking "Add to archive...". If you do it this way make sure you check "ZIP" instead of "RAR" before clicking ok. A zip file with the same name as the folder should appear in the same place you have the folder. This zip file is your texture pack, and it is what you will give to other people. To use it, go back to the appdata folder again, and just put the the zip file in the "texturepacks" folder inside ".minecraft".
It's also worth mentioning that you can add a 128x128 picture in the same folder with "terrain", called "pack". This will be the icon that shows up in your list of texture packs in the game. However, this is optional (I'm pretty sure it will default to the original icon if you don't make one).
If you didn't download WinRAR there are other programs that can unzip and zip files, like 7ZIP but this is the way I would do it.
Well, I guess I typed up a whole tutorial on how to make the texture pack. Not sure if you needed all that, but I hope I helped.