Had an online assesment first then got called in for a group interview. We had to talk to and then introduce the person sat next to us to the rest of the group and then we watched some ASDA company information videos (not sure why, they didn't ask any questions about them). Finally we did a group based task where we had to build a tower of cards, was pretty simple, they just want to see how you work with other people.
Then I got called back for a second one-to-one interview in which I had to complete a knowledge, attitude, hazard perception and risk assesment with regards to driving. Some of the knowledge questions were a bit tricky but they're all multiple choice so it's not too bad. After scoring either low or medium risk on this test you'll go for a one-to-one interview (If you get a high risk score then I imagine they don't hire you) with a section manager which was all very informal for mine. The section leader basically asks why you want to be a driver, what experience you have of working in a team, getting on with people you don't like, and explains a bit about the job. They also check with the DVLA that you don't have any points on your licence.
After this they call you back and let you know whether or not you got the job, I got called back about 4 days later.