I started sewing for my fur babies because I just have always wanted to design and sew things ( I went to school for fashion merchandising/design)... but I'd never actually taken sewing classes.
I started sewing my little girl Emma some things by hand and then progressed to buying a machine from Walmart and I just kept sewing for months, until I finally got something that worked. I'm 100% self taught, and I have to say that after 6 months I an produce a very high quality item.
It wasn't easy because in my case, it took a lot of patience and practice, but I love it so much that it was fun even when it was frustrating. I'm so glad I stuck with it though, because I'm so proud of the items I'm making now.
My advice if you truly want to get started is to buy or check a book out from the library on sewing (preferably one that has a lot of pictures).
Get familiar w/the different "sewing terms" or the lingo and read the book, or at least the sections that apply to what you're doing.
Also, I'd get the best quality machine you can afford if you really want to do it long term. I was working on a 75 dollar brother, and just last weekend purchased an 800 dollar machine and I have to say that it is worth every penny. The efficiency is so much better. (I'm not saying you have to go that expensive at all, but I'd get the best one you are willing to pay for).
Buy cheap fabric to practice on, and just work on it! It is a huge market to get into, and I'd love to build my small business into something bigger eventually, but a lot of it is knowing how and where to market your items
I wish you the best of luck w/it.. sewing is definitely FUN!