Learn Russian: Хлеб свежий, но сыр старый. - The bread is fresh, but the cheese is old.

но is used for a direct contrast or contradiction, often with a sense of opposition (the bread is good/fresh, but the cheese is bad/old). The word а is used more for simply comparing two different things or shifting the topic, like "I have bread, and/but you have cheese."

Do I always need a comma before но?

Yes! In Russian, you must always put a comma before conjunctions like но (but), а (and/but), потому что (because), and поэтому (therefore).

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

In Russian, the present tense of the verb "to be" is almost always dropped. Instead of saying "The bread is fresh", you literally just say "Bread fresh" (Хлеб свежий).

Both свежий and старый are masculine adjectives. Why does one end in -ий and the other in -ый?

This is because of a common Russian spelling rule. You can never write the letter ы after ж, ш, ч, щ, г, к, or х. Since свежий has a ж, we must use и for its ending instead of ы.