One of the most common methods used to invest in early stage startups is something called a convertible note. A convertible note is a loan that converts into equity after the company has a bit more operating history under its belt and there is more information available to establish a fair price.
Convertible notes are often used for seed rounds (the first investment money taken by a startup) because they delay the difficult task of deciding how much the company is worth to a later point in time when it is easier to do so. How much would you say that 2 software engineers and a prototype is worth? How would that change if there was an MBA on the team? By investing through a convertible note, these decisions can be delayed until a company has a track record of users or customers that make it clearer what a fair price should be.
When you invest through a convertible note the startup receives the money right away, but the number of shares you are entitled to is determined during its next round of financing, or Series A. At that point the company will have some operating history that more experienced angel investors or venture capitalists can review in order to determine a fair price. Once the series A investors have determined a price, your loan converts into shares at a discount to the series A price to reward you for the additional risk you took on by investing early.
The amount of equity that a note converts into depends on the price of the A round plus 2 key components of the your note.
Convertible notes generally convert using the the discount rate OR the valuation cap, whichever gives the investor a better price. Lets say the note has a $3 million cap with a 20% discount and the company receives a $6 million series A valuation at $1 a share. In this case using the discount rate would yield a price of $1*.8 = $.80 a share, and using the valuation cap yields a price of $3 million / $6 million or $.50 a share. $.50 is a better price so we use the valuation cap. If the series A valuation had only been $3.5 million at $1 a share using the discount rate still gives us a price of $.80, but using the valuation cap give us a price of $3 million / $3.5 million or $.86. In this case $.80 is a better price so we use the discount rate. It is important to note that the discount rate and valuation cap do not both apply, only the method which results in the best price for the investor.
It is hard to determine if convertible note terms are fair when you do not have much investing experience. Ideally an experienced investor will already have invested in the company and set the terms. If not, you should look at startups with similar teams and traction, and see if the startup you are evaluating has similar terms.
A much more in depth treatment of convertible note financing from an entrepreneur's perspective can be found here:http://techcrunch.com/2012/04/07/convertible-note-seed-financings/