There are a couple of different ways to go about this, depending on what you want at the end. Most importantly, there is no way to change the process template from one to the other inside a Team Project, so you'll have to create a new Team Project with the Scrum Template to migrate to.
If you want history & attachments:
Then you need to use the TFS Integration Platform. You'll create a xml mapping to flow the work items and source code from one project to the other. There are quite a few issues with going this direction including, history is compressed, the tool is notoriously finicky, shared steps (and other things) don't migrate and more. This is definitely not the recommended option, but sometimes you don't have a choice. Here's where to get the tool: http://visualstudiogallery.msdn.microsoft.com/eb77e739-c98c-4e36-9ead-fa115b27fefe
If don't need history, or can keep the other Team Project around: For this method, moving the code is easy (it's even easier if you've got a Git project, and you'll get history. Use the git-tf functionality to move your source to Git). Just check out from one repository, switch your workspace mapping and check in to the new repository.
To move your work items, use work item queries and export them to Excel. Then copy/paste into a second Excel spreadsheet and upload them to the new Project. This is by far the easiest method. Here's a detailed explanation:
1) From Agile template project: for each work item type that you want to move, create a work item query to pull all the ones you want and export them all to Excel (for example a query to pull all requirements and another for tasks)
2) From the Scrum template project: create a work item query for each work item type that you want to import and export it to Excel. It's going to be blank, but you're going to use this Excel spreadsheet to upload in a minute.
3) Copy/past from one Excel spreadsheet to the other, being careful to NOT copy column headers. A neat trick is to copy the History column from the old project into the Comments field in the new project.
4) Publish the results. Viola, you're migrated.
Best Answer
TFS can be very confusing when it comes to sprint ends.
I have found that the best way to make it work is to ensure that you have several sprints configured, with the end date of one being followed the day after by the start date of the next.
If there is a gap between the sprint dates then the previous sprint stays 'current' up until the day on which the next sprint starts.
So something like this:
Note that there is no manual way to close a sprint. You have to do it with the dates.