Regularly, you add a σ at the end of the stem. The σ almost always interacts with the last letter of the stem, though, so there are further rules there. In sakeldon's example, διαβάζω, ζ+σ->σ, so it becomes θα διαβά(ζσ)ω->διαβάσω. For γράφω (write), φ+σ->ψ, so θα γράψω = I will write.
However, I'm afraid that all verbs up to this point, except for διαβάζω, are irregular. In this case, the stems are usually related, but not in the above way, so you have to memorise them. A few examples, πίνω becomes θα πιώ, βρίσκω (find) - θα βρω (I will find), δίνω (give) - θα δώσω (I will give), τρώω - θα φάω (I will eat, totally unrelated stem).
The comments on this sentence seem to imply that "θα" specifically shows the future progressive, not just the simple future. If that's true, shouldn't my answer of "I will read" not have been accepted? If the point of this sentence is to introduce this conceptual distinction to us, I feel like it should be made clearer.
As rxan90 has written above, θα is used for all future and conditional tenses. Θα + present tense gives the future progressive. You need to add other forms after θα to get the simple future, the future perfect or the conditionals. It is just like English, where you add different things after "will" and "would" to get different meanings; θα means either "will" or "would", depending on what comes next.
Nothing against the sentence itself, but how it appears. I don't remember ever having seen this form before, and it just pops up as "write what you hear" sentence. I actually try to figure out what it means I hear, and not just type down the sounds I hear. So, I am thinking that Greek is really unclear and muddled, everybody mumbles, and it's up to the listener to guess what they are saying. Which is what I do most of the time anyway. It was really a huge surprise to visit 50languages.com and hear people enunciate properly... And then it turns out that the reason to why I don't understand what they say is not only because they are unclear, but because they say things I couldn't possibly understand. sigh