How do I tell Beeminder what day my week starts?
The answer is that that's the wrong question!
Beeminder doesn't care when you do the work; it just forces you to stay on the good side of the bright red line every day. If you start the goal Monday, you can do all your work Monday and coast the rest of the week, but you can't procrastinate and make up a week's worth of work on Friday. You don't necessarily have to work a little every day if you've already done enough work to stay on track for awhile. Just that if you ever end the day on the wrong side of your bright red line, you'll derail.
When you create a new goal, you can opt to start with some initial days of safety buffer. If you have a goal to, say, call your parents once a month (and you already called them yesterday), start the goal with 30 days of buffer. Visually you'll see that as a long initial flat section of the bright red line on the graph. And staying above that line means that your overall average rate of calling your parents can never fall below once per month. Calendar months don't matter, just the overall rate.
Here's another, more common, example. You start a "6 workouts per week" goal on Monday. The average pace for this goal would be about 0.86 workouts per day (6 workouts divided by 7 days in a week). If you do one workout per day for the first six days of the week, you'll earn a day off on Sunday. You can do all 6 workouts on Monday and coast the rest of the week! (Not recommended.) But you can't procrastinate and make up a week's worth of workouts on Friday, because you'll have fallen below the average pace before then.
If you want to align your weekly schedule to M-F, add enough initial safety buffer so that your first beemergency is next Monday. That'll give you some extra days to get over an irregular first week schedule — for example, if you started the goal on Thursday.
(We get this question a lot, which means we need to do a better job of making it clear up front, but in the meantime, we have this help page to point you to! There's also an ancient blog post describing these types of "chunky" goals.)