Learn Swedish: Vi hade knappt tusen besökare sammanlagt. - We had just under a thousand visitors in total.

In Swedish, knappt before a number means "just under" or "slightly less than". It is the opposite of drygt (just over). So knappt tusen means they were very close to a thousand, but did not quite reach it.

Is besökare a singular or plural word in this sentence?

It is plural here, because of the number a thousand. Nouns that end in -are (which usually describe people or professions, like lärare or besökare) are tricky because their indefinite plural form is exactly the same as their singular form. One visitor is en besökare, and a thousand visitors is tusen besökare.

Can I say ett tusen instead of just tusen?

You can, but it sounds a bit overly specific. In Swedish, it is most natural to just say tusen for "a thousand" and hundra for "a hundred", unless you need to strongly emphasize the number one.

How is the word sammanlagt built?

It is put together from samman (together) and lagt (a form of the verb lägga, meaning to put or lay). So it literally translates to "put together", which is used here to mean "in total" or "altogether".