It's a fucked up system. Even the pricing is even worse, Court 2 is only like £10 more than Centre Court for the first week or so, that's just messed up.
Just go on Ticketmaster the morning before (there's a specific time) and there are 500 tickets remaining for a few courts including CC, it's hard to get the tickets but providing you do it right you'll get them. Also better as you'll have a rough idea of who's going to be playing on the main court those days.
In answer to the OP, yes, it's a random day and a random court. You get offered two tickets, take it or leave it. They can get away with this because it is always massively oversubscribed.
The info about Ticketmaster will work fine if you live an easy distance from Wimbledon. If, like me, you have to arrange train tickets and hotels, it's no good at all. It's the only time of the year that I'm really jealous of people living in the south of England!