different ways to save money?

At 13, babysitting and odd jobs (shoveling snow, mowing lawns, yard work) are perhaps the best ways to make money. You can ask your parents friends or around the neighborhood (with your parents permission, of course). If you do any kind of crafty thing very well you could try to sell it, or if you could garden and sell produce at a farmer's market, you might be able to pick up a little money that way. Some kids around here do pretty well with raising animals for 4-H and selling them at the fair, if you have the right yard for that sort of thing (some animals, like chickens for eggs or bees for honey, work in a few more places).

For saving, you should open a savings account -- try to find one with no fees, set up for kids, maybe at your parent's bank. If you put the money there, it is harder to get out.

Also ask your bank about savings instruments like CDs, or certificates of deposit, that will hold your money for a length of time (6 months, 2 years, or longer) and give you a higher interest rate. The money that you are saving needs to earn money in interest or it will lose something called buying power. You might have heard of inflation? Inflation is when things cost more and more money each year, so you need more money to buy them. Inflation isn't much -- usually around 3% each year. But after 10 years, something that costs $10 today would cost $13. So if you have $10 today and put it in the mattress, you'll just have $10 in 10 years, when that thing costs $13. But if you put it into a better savings option (like a CD) you would have $14 or $15 in 10 years. You can ask at your bank for other options, or your parents could help you look into online banking.

I'm assuming your parents pay for most stuff so saving shouldn't be too hard... it's getting the money that's probably tougher for you.

You could start your own business - make something and sell it (like cute dog collars or something and then go to the local dog parks and sell them to the owners), sell something that already exists (like sell cold Cokes and Diet Cokes to people at a local park), provide a service (like charge people to help decorate their houses at Christmas or wrap gifts, or do manicures at a convalescent home or whatever), or...

work for someone else (dog walking, house cleaning, house sitting, car washing, etc).