Learn Finnish: Kiittäisitkö seppää kauniista alasimesta? - Would you thank the blacksmith for the beautiful anvil?

The verb kiittää (to thank) requires the person being thanked to be in the partitive case. This rection rule gives us seppää from the nominative form seppä.

Why are the words for beautiful anvil in the elative case (kauniista alasimesta)?

This is another specific rection rule for the verb kiittää. The thing you are thanking someone for must be expressed in the elative case, which ends in -sta or -stä. While in English you thank someone for something, in Finnish you conceptually thank them out of something.

What is the base form of alasimesta and why does the stem change?

The base form is alasin (anvil). Nouns ending in -in change their final -n to -m- and add an -e- before any case endings. Therefore, alasin turns into the stem alasime-, to which the elative ending -sta is attached.

How is the verb Kiittäisitkö constructed here?

It starts with the verb kiittää. We add the conditional mood marker -isi- and the second-person singular ending -t to make kiittäisit (you would thank). Finally, the question particle -kö is attached to turn it into a yes-or-no question.