How much equity do I give an investor?

Take on $20k as convertible debt.

You will be taking a loan for the money that will convert to equity on the next round of fundraising. This will give you time to develop your company and figure out what it could be worth. If no further funding is required, just repay the note + interest from the revenue and keep the equity.

Good article on Venture Hacks quoting Chris Dixon: http://venturehacks.com/articles/amount-seed-money

To your question, he's saying that assuming 20k is "as much as possible" in terms of how you've decided how much to raise, keeping your dilution to less than 20% is ideal. Assuming you go through multiple funding rounds - you won't want to give up too much too early, especially if your first round is fairly small.

Give them a hot dog, and a diet coke!. Give them as little as possible. 20k is a small amount of money. If your startup only requires 20k to go to market, (development, testing, hosting, initial marketing), and you are sure that the 20k is all you need, then you should seriously look at funding the startup yourself.

The answers citing percentages of the total equity are actually absurd because, at the time of writing, we don't have enough information to cite a percentage (nor an upper or lower bound). I don't yet have the rep to down vote.

The answer is both trivial and impossible to do precisely: Just estimate the sum of the present value of cash flows to be generated by the business, discounting each cash flow for time and uncertainty before summing. Since you're at an early stage the discount will be large. Suppose the sum of present values is X dollars. Then $20,000 divided by X dollars is the fraction of equity that $20,000 will buy. If you need more details on how to do this, just pick up a finance textbook like Brealey Myers.

That said, Tim's suggestion about accepting a debt investment is something you also might consider. Debt might be attractive to the investor because it's a "more-solid-than-equity" obligation of yours and you get to keep more control. Thus, it could be a win-win (but only if both sides think it is a win-win). If you're in a bamboo shack in the southern Philippines, $20k is a lot of money but otherwise may be you should just come up with the money yourself as Frank wisely suggested.

As there are currently two answers not answering the question at all, I will offer you my bid. I would offer them 20-30%. I do not believe that you would get anyone (other than relatives) to only get a 10% stake for any investment, which is so small. There will, after all, be some work for them to check up on you.

Usually magic figure will be somewhere around 26% and not more than 26% and this is what i saw in many VC deals so i feel you can go around 20 - 26 . My sincere suggestion is go to investment banker and valuate your product so that it would be easy to decide on percentage. But better build atleast a prototype in order to make valuation.

If it's an early stage startup (with no revenues / customers) - settle for 20%. Also, I hope the investor is going to add significant value to your startup

Yeah overall $20K is very small and if that's all you need to make it a company that is potentially worth million I would be worried about several points:
1 - Could anyone else with $20K replicate your idea and bit you? Basically, do you really have a competitive edge. If the potential is millions, you are not going the only one on it so try to be careful.
2 - If you feel that the investor is asking too much equity, then it's too much. An investment is related to a value. In the end, you are the owner of that value and should feel comfortable that the money you receive is worth the equity you give. In one of the comment you say "what if that's the only way to get $20K", well if the idea is good, there will be other way (and convertible notes are definitely a good thing to look at).
3 - Try to forecast different rounds of investments over time and understand clearly dilutions, preferred shares, etc.. Know that new investors often change all the terms you have created in previous agreements.

Anyway, you are at the idea stage.. Try to build a business plan, it's a good exercise and should contain financial (revenue, value, costs, etc..). $20K won't take you very far, so don't give equities, or if you do, give very little.

It depends on a few things. First thing how much is the investor putting into the company? I would highly encourage you for items such as these to be working with a legal firm that will have all of these estimates and be able to calculate a fair percentage for all parties involved.

Tim's suggestion to do a convertible note is very wise.

You can structure a convertible note so that it's never repaid in cash; at maturity or default it can be convertible into common stock, and you can just pick a low valuation of the company then.

I don't know where these people are getting their education from.
For such a small amount of money you should try to get a loan. Even if it's high interest you'll be able to pay it back quite quickly (provided your idea IS indeed a good one!), and you won't have to give up any equity. Just do the math. Even if you're paying 20% interest on your loan (a very high estimate) you're only paying that once as opposed to losing 20% or more of your profits forever.