Ways for teen girl to earn and save money?

Typical and obvious jobs for teenagers include:

working at a fast-food restaurant
working as a clerk in a store
working as a bag boy at a supermarket

or if you are not old enogh try this:

Baby-sitting - Babysitting is a tried and true way for any responsible teenager to make money (IF you like kids!). Any community that has families with small children needs baby-sitters. However, it is extremely hard to find trustworthy and reliable baby-sitters who are available on a regular basis. Your business would provide in-home baby-sitting services. There are several things you can do to make your services more valuable. First, you should go take a Red Cross first aid course so that you know how to handle emergencies. You might also want to volunteer at your church if there is a day-care center there. You can pick up a lot of valuable experience that way. Second, you might want to consider teaming up with some like-minded friends. That way your group will be able to say "yes" more often and that will increase the number of calls you get. See this page for some great advice on babysitting.
Lawn or yard care - Another perrenial favorite. During the summer you mow lawns, trim hedges and so on. In the fall you rake leaves. In the winter you shovel snow.
Indoor house painting - You advertise your ability to paint individual rooms in a customer's house. Before undertaking this adventure you should make sure you know what you are doing by reading, working with someone with experience and practicing in your own home.
Baked goods (cookies, cakes etc.) - Many families are too busy to bake their own cookies and cakes these days. However, having fresh-baked goods around the house is nice. Also, a family might need a home-baked cake for a school bake sale or a party. You could provide baked goods for special occasions like these or sell baked goods at local craft or farmers' markets. Check local health laws as you are starting this sort of activity.
Cleaning - If you enjoy cleaning and do it well, then house cleaning for others is straightforward and easy. Find busy people in your neighborhood and clean for them once every week or two.
Dog walking or vacation pet care - Most people who have pets want to give them the best care possible. Your business would help pet owners to do that by walking their pets daily or by providing in-home pet care when owners are on vacation.
Errand-running for busy people - Busy people often do not have time today to stand in line to get their license plates renewed, to buy groceries or to run other errands. Your business would handle these tasks for them.
Washing cars for neighbors - You can simply wash cars. There is also a whole industry called "car detailing". A detailer washes and waxes the outside and REALLY cleans the inside: vacuuming, washing the windows, armor-alling, etc.
Teaching older people how to use computers or the internet - Many older people are totally affraid of computers. If you understand computers you can help them. You could come to the customer's home (or they to your home) and you could charge on a half-hourly or hourly basis.
Using a computer application - learn Microsoft Word, Excel, PowerPoint, Access, etc. and then go get or create a part-time job in a small business using your skills (see also the Job Skills article).
Creating Web Sites - If you are artistic and technically minded, there is a great opportunity available right now creating web sites for small businesses. Or try creating your own web site that generates a lot of traffic and make money selling ads on it. (see also the web site article)
Making and selling something unique: A newsletter on something that interests you, something arty, etc. If you are artistic create greeting cards or draw portraits. You will discover that your greatest difficulty doing this is finding outlets, so work to solve that problem (you will learn an incredible amount in the process).