Learn Danish: Han ser mig ikke. - He does not see me.

jeg is the subject pronoun ("I"), while mig is the object pronoun ("me"). Since "he" is the one doing the seeing, he is the subject (han), and "me" is the one being seen, making it the object (mig).

Why is ikke at the very end of the sentence? Shouldn't it be "Han ser ikke mig"?

In Danish, short object pronouns like mig, dig, and ham usually jump in front of ikke. If the object was a regular noun, it would come after ikke (for example, Han ser ikke hunden - "He does not see the dog"). But because mig is a short pronoun, the order becomes "he sees me not" (Han ser mig ikke).

Where is the word for "does" in this sentence?

Danish doesn't use "do" or "does" to make negative sentences. Instead of saying "He does not see", you just use the verb and ikke to say "He sees not" (Han ser ikke).

The word mig ends with a "g". Is it pronounced?

No, the "g" in mig is silent. The whole word is pronounced very much like the English word "my".