What's a good software development methodology to follow for a project where you initially know nothing. So an experimental project where you will need to seek out APIs and so on as you carry out research and figure out what needs to be created.

I'm required to follow a design methodology but Waterfall and all such methods I've looked at require a complete design then implementation. Whereas I would need to design several things, implement them to test which ones work, then possibly redesign again....

Please help!

that depends on how you want to develop, and usually the right choice for one project, isn't the right choice for another project.

Some examples would be nice.