Learn Swedish: Min mamma gör en varm smörgås. - My mother makes a warm sandwich.

Because smörgås is an en-word (en smörgås). When describing a singular en-word, adjectives keep their base form. If it were an ett-word, like ett äpple (an apple), the adjective would add a -t to become varmt.

How do I know to use min instead of mitt here?

The word for 'my' has to match the noun it belongs to. Since mamma is an en-word (en mamma), you use min. If it were an ett-word, like ett barn (a child), you would use mitt.

Could I use lagar instead of gör for making a sandwich?

Swedes usually use gör (makes or does) for simple preparations like assembling a sandwich or making tea. The word lagar is generally saved for actually cooking a meal, like in the phrase lagar mat (cooking food).

What happens to the adjective if she makes more than one sandwich?

If the noun becomes plural, the adjective gets an -a at the end. 'Warm sandwiches' would be varma smörgåsar.