Everything Juulie said is spot on, as usual.
I also check the scoreboard a bit more frequently at the end of periods as a way of anticpating what might occur. For example, a team down 1 with less than a minute to go is going to try to execute differently than a team down 3 or 5 with the same amount of time. Plus, it reminds to look to the coaches for possilbe timeouts.
I guess to address the mechanics point of your question, how you do it is really up to you. I always glance at the board after a made basket as I transition into my new position. Some of our gyms only have a scoreboard at one end, so that can change things, but do it the easiest way you can that doesn't take away from your ability to officiate the players.
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