Learn Finnish: Lopuksi kiitämme kaikkia vieraita. - In closing, we thank all the guests.

While you likely first learned the translative case (ending in -ksi) to show a change in state, it is also heavily used to form adverbs indicating a sequence or role. Here, lopuksi literally means "as an end" or "in closing". Other common examples of this sequence building are aluksi (at first) and seuraavaksi (next).

The object of kiittää is in the partitive here. How would we add the reason we are thanking them, like "for their visit"?

The verb kiittää takes the partitive case for the person being thanked (kaikkia vieraita), but it requires the elative case (ending in -sta or -stä) for the reason. To say "we thank all the guests for their visit", you would say kiitämme kaikkia vieraita vierailusta. This is a highly useful verb rule to master at this level.

How is the partitive plural vieraita formed from the base word vieras?

Words ending in -as or -äs have a long vowel stem ending in -aa- or -ää- (which you see in the genitive singular vieraan). To form the partitive plural, you take that strong stem vieraa-, shorten the long vowel by dropping one a to make room for the plural marker i, and add the partitive suffix -ta. This creates the form vieraita.