Learn Swedish: Företaget byggde en maskin till projektet. - The company built a machine for the project.

The verb bygga belongs to Group 2a. To get the simple past tense (preteritum), you take the stem of the verb, which is the infinitive without the final -a (bygg-), and add -de. This gives us byggde. Group 2a verbs take the -de ending because their stems end in a voiced consonant.

Why is till translated as "for" here instead of "to"?

While till is frequently used for physical directions (meaning "to"), it is also the most common preposition used to mean "for" when talking about a recipient, a purpose, or an intended target. Because the machine was intended for the project, we say till projektet.

Why do the words företaget and projektet both end in -et?

They are both ett-words (neuter nouns): ett företag (a company) and ett projekt (a project). To say "the company" and "the project" (the definite form), you simply add the suffix -et to the end of the word.

If I start this sentence with a time word like igår (yesterday), how does the word order change?

Swedish strictly follows the V2 rule, meaning the verb must be the second block of information in a statement. If you put igår in the first position, the verb byggde must come right after it, which forces the subject to move: Igår byggde företaget en maskin till projektet.