Otan avaimen pöydältä ja lähden kotiin.

Finnish verb endings show the person, so the subject pronoun is often unnecessary.

• otan = I take (1st person singular)
• lähden = I leave / I go (1st person singular)
  You can add minä (Minä otan…) for emphasis or contrast, but it’s usually omitted in neutral speech.

avaimen is the object in the so-called total object form (traditionally described as accusative; in many singular contexts it looks like the genitive -n). It suggests a complete, bounded action: you take the/that key (one whole key), not “some key” or “keys in general.”

• Otan avaimen. = I take the key (one whole key, action completed)
• Otan avainta. (partitive) = I’m taking a key / I take some of the key / I’m in the process of taking it (depends on context)

Formally it looks like the genitive singular (-n), but functionally it’s used as a total object (often taught as “accusative object” in Finnish grammar). In practice, learners can remember:

• -n object (like avaimen) = total/completed taking
• partitive (avainta) = partial/ongoing/indefinite taking

pöydältä is pöytä (table) + -ltä/-ltä = ablative case, meaning from (off) a surface.

• pöydällä = on the table (adessive, location “on/at”)
• pöydältä = from the table (ablative, movement away “from off”)
• pöydälle = onto the table (allative, movement “onto/to”)

So Otan avaimen pöydältä is literally “I take the key from off the table.”

They’re both “from”, but with different spatial ideas:

• pöydältä (ablative) = from a surface / from off the table
• pöydästä (elative) = from inside something (like talosta = out of the house)

A table is usually treated as a surface, so pöydältä is the natural choice.

kotiin is the illative case, meaning into / to (home), i.e. movement toward home.

• kotiin = (go) home, to home (movement to)
• kotona = at home (location)
• koti = home (dictionary form; not the correct case here)

So lähden kotiin = “I leave for home / I go home.”

They’re present tense, 1st person singular, and both show common stem changes.

• ottaa → otan
  
  • double tt becomes single t in this form (a type of consonant gradation)
• lähteä → lähden
  
  • t changes to d in this form (another common gradation pattern)

These changes are very typical in Finnish verb conjugation.

Yes, ja is the standard word for and. It links two equal parts:
Otan avaimen pöydältä + lähden kotiin.

Word order stays quite flexible in Finnish, but this is a very neutral, common structure: [verb + object + place] ja [verb + place].

Yes. Finnish allows reordering for emphasis or style.

• Otan avaimen pöydältä… (neutral: focus on the key)
• Otan pöydältä avaimen… (slightly more focus on from the table)

Both are grammatical; context decides what sounds best.