Angels are private individuals or groups who are interested in helping entrepreneurs get started. They could be family and friends, former entrepreneurs who made good, or groups of private investors who can pool their monies. Family and friends typically will offer small amounts of money. Former entrepreneurs will often provide $25K-$50K to get you started. More successful ones who believe in your company might go as high as $100K. Angel Funds may go as high as $250K to $500K.
Although it's tempting, I'd advise you to avoid family and friends if possible. You don't need Uncle Jim, who made money selling used cars, telling you how to run your business. And, you don't need the guilt you'll feel if you lose the money that Aunt Mary invested.
So assuming you're going to take money from a 'Qualified Investor' (someone who is considered knowledgeable and able to afford the risk), in general, you should be prepared to give up about 25% of your company for your first angel/seed round of investment where you raise $250K-$500K total.
Experienced Angels can be very helpful. They've been where you are and most are looking to 'pay back' a bit of their good fortune. They can provide business advice, introductions to customers and other investors, and they usually have a lot of credibility in the market and the investment community.
Your choices for structuring the deal generally fall into convertible debt where the investment is considered a loan, but a loan that can be converted to equity at a later date, and equity where the investors will own shares of your company, usually preferred shares.
Convertible debt means that you take loans from the investors but that they will have the right to convert to equity at some time or event in the future (e.g. you decide to raise a Series A round from VCs). Pricing that conversion can be tricky. A bit more on that below.
Offering equity is a bit more complicated than taking a loan. You need to create a preferred class of stock and structure the preferences, including voting rights, board seats, liquidation terms, terms for converting to common stock, and more.
While I'm thinking about it, let me advise you to be careful with liquidation preferences. In general, VCs and Angels will ask that their investment be repaid in the event the company is liquidated. The problem lies in the definition of 'liquidation'. As an entrepreneur, you're probably thinking that if the company goes under, it's only fair to let the investors get as much of their money out as they can. However, in most cases, 'liquidation' also includes sale of the company. In an upside sale (as opposed to closing down the company and selling off assets), this means that you pay back the investors, then they convert their preferred stock to common and share in the remaining proceeds of the sale. I call this the 'double dip'. Avoid it if at all possible.
Coming back to equity versus debt, in general taking a loan as convertible debt works better for you than giving up equity. However, if your angels are helping your company in a big way, it seems only fair that they should share in the equity up front and not have their upside limited in the debt conversion.
The most challenging part of either convertible debt or equity is valuation. While most of us would like to value our companies high, thus giving up less equity now (with equity funding) or later (with convertible debt), valuing too high can be a dangerous trap. It may cause you to give up much more of your company with future investments if you haven't proven and increased your valuation, and for the convertible debt, the conversion may cost you hugely.
If you gave your Angels equity, they share in your downside by being diluted. If you gave them convertible debt, their conversion would be at the new rate and they would have more of the company.
So, be careful with valuation. For a great article on Angel Funding, which is still relevant, if a bit old, see Mark Suster's Angel Funding Advice.