If you just want to change the sprites, no real programming background is needed. However, knowing programming will give you a better grasp at what is going on.
The tile editing program I recommend is Tile Molester*. However, it's usage can be described as "unintuitive" for a beginner. If it's too difficult to use, there are other programs like Tile Layer Pro or YY-CHR, although they do not offer the same functionality as Tile Molester.
First, you need to find where the sprites are stored in the ROM. That's basically finding the right settings to use in the tile editing program you are using, and scrolling down the file. You will see stuff that looks like TV static, but that is game code. If the sprites are uncompressed, you should be able to see the sprites among the "static", although discolored.
To view (and edit) them with the right colors, you need to extract the palette. This is retrieved by playing the game and getting to a point where the sprite you want to edit is on the screen. Make a ZSNES savestate. Then load that savestate into the tile editing program, and go through the different palettes contained in the savestate file. You should be able to find the right one.
*Using Tile Molester on the Sailor Moon girls sounds like the premise for some hentai doujinshi.