Explore the cutting edge. What are the front-runners doing, and what problems are they addressing? The cutting edge is known for being risky because nobody is sure of the best solution. Look at the problems that they are addressing and add those to your list. With any luck, you can think of a better idea.
Step 2: Understand the Technologies
The more you understand the tools available to you, the more effective you will be at finding creative applications for them. Ideally, you want to get to the point where you can have an intelligent conversation with a programmer, but for now it is enough to just have higher-level knowledge.
For each technology you think you might be able to use, figure out:
How it works. While you don't have to be able to program, you really should have a general idea of how the magic happens. So long as you know what the tool is called, you will be able to find an accessible guide. Just remember that Google is your friend here.
What it does. Tools tend to have an intended purpose, although often it's a very broad one. Be sure to understand what that purpose is. You can start by looking at its website and see what its creators say. Also try to find out which existing sites have used it, and examine what they have done.
What it could do. Once you get a basic understanding of a tool, you can start to get creative and think of ways to use it that its creators never would have thought of. This task is all on your shoulders, but you can always scour tech blogs like TechCrunch or SlashDot to find examples of how people can push the limits.
If the technology is at all popular there is probably a community surrounding it. Once you find it, create an account and join the party; there will be people willing to help you learn.
Step 3: Imagine Solutions
You have a list of tools and a list of goals, now it is simply a matter of creative application: find out how to achieve those goals with the technologies available. Brainstorm as many solutions as you can for each problem, and be sure to dream a little bit here.