Just so you know what to look for, at the end of your Summary period, you’ll receive an entry in your account feed which looks like this:
Tap on ‘Spending report’ and you’ll see a display which shows a quick breakdown of your activity during the last period. The big blue number at the top is how much you have left. If you then tap on ‘ADD TO POT’ at the bottom, you’ll be able to move that amount from your account into a chosen pot:
I don’t have a budget set, so it appears it works the same for people who do or don’t have budgets set.
EDIT: If you haven’t been paid yet, you probably won’t see the Spending report feed item until a month after you have been paid because Monzo won’t know the period to base a Summary report on, which usually starts with a receipt of income.