IMPORTANT! Limited Partners can be persons or corporations, or even other limited partnerships. For maximum protection, we suggest your limited partners be corporations. Click the "?" icon for more information.
Your Limited Partners are meant to be passive investors and don't take an active part in the business. They invest money into the partnership hoping to make a return by getting some of the profits from the partnership, but they leave it to the General Partner to run things.
Since they're passive, the Limited Partners are only responsible for partnership liabilities up to the amount of their investment. So if you put in $10,000 into the partnership as a Limited Partner, that's the maximum liability you have. BUT, there are two big exceptions to that rule that you need to think about.
First, you're still liable up to your investment. You also don't know for sure that you're getting that investment back - if business doesn't go well, it may not have that money to give back to you when you wind up the partnership. So, it's safest to think of being at risk up to your investment amount.
Second - and more importantly - if a Limited Partner is actively involved in running the partnership's business, that partner becomes fully responsible for the liabilities of the business. So if you slip up and are too active of a Limited Partner, you could be in trouble.
Advanced tip: to protect yourself, the safest option is to use a corporation (sometimes called a "holding company") to hold your Limited Partner investment. That way if you do slip up and become liable, your corporation is the one responsible and not you personally. However, you'll have to trade that off against maybe getting a better tax outcome if you hadn't used a corporation (something to check on with your accountant).