Community Manager Nethaera filled in some of those blanks in a series of updates posted on the official forums. The first two realms that have been scheduled for connection are Boulderfist and Bloodscalp. The system will be rolled out over time, much like what we saw with the Cross-Realm Zones feature -- players won't suddenly see all realms introduced to the Connected Realms feature all at once. Blizzard intends to keep realm types together as much as it possibly can -- for those on RP realms, this means if your realm is connected to another, it will likely be another RP realm.
Nethaera went on to note that faction balance, something that has caused many players to struggle on incredibly lopsided realms, may not be the ultimate reason for a connection. But perhaps most importantly -- as of Friday, no realms have been connected. Any server restarts or messages about Connected Realm restarts in game are absolutely not an indicator that your realm has been connected to another -- it's simply some of the work that needs to be done in order to enable the connecting process, should it need to be utilized. For now, it seems that players are still isolated on their own realms -- but there should be further updates to the thread if that changes. For more information on the implementation of this new feature, check out the thread on the official forums.