Frank make a good point in his comment to my previous post. He told me he had to look up the term "mordant," so I thought I'd quickly explain what a mordant is. Some dyes, called substantive dyes, can dye a fiber on their own, without addition of other chemicals. Many dyes, especially natural dyes require a mordant, a chemical that bonds to the fiber and to the dye to make it wash- and light-fast. The most common mordants are metal salts - I usually use alum, because it is the least toxic and simplest to use. All mordants can have an effect on the final color and wash and light-fastness (meaning how well it holds up to exposure to UV light and washing) of the piece. Clearly there is a lot of science here that I'm not familiar with - maybe someday it will be more interesting to me, but at the moment I'm more interested felting than dyeing.
My friend Heather also just asked me a question about good dyes for yellow and red on silk. She said she had heard turmeric makes a yellow dye, and it does, but it isn't very light-fast (and might not be very wash-fast, I'm not sure). Onions skins will make a variety of yellows, depending on the type of onion, and they don't require a mordant. Red's a little tougher - it's hard to find common household items that make good reds. I've heard dandelion roots work but that it can be hit or miss, and isn't exactly a household item. I would say the best bet would be to get some alum and some brazilwood extract or lac if you want to use natural dyes. If it isn't especially important to use natural dyes, you could always use an acid dye, which in this case might be simpler and quicker to use.
The Art and Craft of Natural Dyeing by J.N. Liles is a great resource for natural dye recipes...Unfortunately I can't find my copy right now, but it includes a whole chapter on different mordants and chapters on dye recipes in all the colors of the rainbow for silk, wool, cotton, and linen. I highly recommend it if you have any interest in learning to use natural dyes or have an interest in the history of natural dyeing.