Okay, I've done some dying in my day (both kinds, I guess!) and I would caution against throwing your hand-knit merino wool cardigan in a hot dye bath. It would probably fit Fifi afterward! Your best bet on dying is to choose materials that will soak up the color, like cotton, jersey and most natural fabrics - but not wool, specialty weaves like taffeta or anything cut on a bias. If it's dry clean only, don't.
It's possible to dye more than one article at a time, but make sure everything swirls freely around in the (hot) water for the specified time, and remember to use more packages of dye. Otherwise your new color will looked washed out and faded. If you want to turn a dark item to something lighter, or white, Rit makes a color remover you use before you start the actual dying process.
Some fabrics may soak up more color than others, but if they're the same hue, they'll match okay. You can even put different colors in together, like khaki pants and a pink tee shirt, and they'll end up basically complementing each other, color-wise. However, I have had fabrics that dyed beautifully while the threads did not! Those are factors you probably can't always guarantee.
It's also fun to mix dye colors to produce hues that are something other than the basic blue, yellow and red you find on the shelf. I mixed a whole load using two reds and two oranges and got a lovely coral shade. And pine green mixed with yellow produced olive.
I just do it in my washing machine at home, followed by washing the pieces in cold water with a little soap afterward to lock the color in and assure they won't bleed later in the regular wash. Then clean the washing machine by running an empty load with soap.
First, though, you can follow the tiny print instructions, or just remember that any stains or dirt will transfer, so you need to Shout out the problem areas and wash your piece first. Hope that covers it! Good luck!