Role of Testers in Agile?

I work in a team which has been doing the traditional waterfall method of development for many years. Recently, we've been told that future projects are going to be moving towards an agile (particularly Scrum) methodology. It so happens that my project will be one of the first, so we will essentially be guinea pigs for the next few months to iron out what it takes to make the transition.

The project itself is in a very early stage and we would usually be many months away from releasing anything to the testing team, but now we are going to be working directly with them up front. As a result, I'm concerned as to the role of the testers in such a project at this stage. I have several questions/concerns which hopefully some experienced agile developers could answer:

While a developer is coding a task, it is impossible for a tester to test it (it doesn't exist yet). What then is the role of a tester at this point
Is the tester now involved in unit testing? Is this done parallel to black box testing?
What does the tester do during a sprint where primarily infrastructural changes have been made, that may only be testable in unit testing?

How do the traditional test team members function in your agile project?

Solution

Keeping testers busy tends to get easier as a project matures (there is more to test!), but the following points apply in the early stages too:

Testers can prepare their test plans, test cases, and automated tests for the user stories before (or while) they are implemented. This helps the team discover any inconsistency or ambiguity in the user stories even before the developers write any code.
In my personal experience, testers don't have any involvement in unit testing; they only test code that passes all of the automated unit, integration and acceptance tests, which are all written by the developers. This split may be different elsewhere, though; for example your testers could be writing automated acceptance tests. Unit tests really should be written by the developers, however, as they are written in tandem with the code.
Their workload will vary between sprints, but regression tests still need to be run on these changes...

You may also find that having the testers spend the first couple of days of each sprint testing the tasks from the previous sprint may help, however I think it's better to get them to nail down the things that the developers are going to be working on by writing their test plans.