Portrait, Landscape or Still Life?
Are you looking at a person (portrait), place (landscape), or thing (still life)? Get off to a good start by using the correct term instead of calling the piece, "a picture."
Form and Line
Shading and texture give an object form, and generally make a piece look realistic. Talking about line is another way to discuss the shaping of the objects in the piece. Are facial features well defined and detailed (if you're discussing a portrait), or more subtle? Form and line also give an object movement or a sense of being static. Use your intuition. It's unlikely that a bowl of fruit will have much movement.
When you've said everything you can say about what's in the painting or sketch, talk about what's not there — the negative space in the piece.
Natural or Surreal?
Take a look at the composition of the piece — aka where the people and objects (the "content") are placed. If they're shaped or interacting with each other in an unrealistic way, you can safely categorize it as being surreal.
Realism, Impressionism, Expressionism, or Abstract Expressionism?
Is the artist attempting to make the content of the work look real, like a photograph? If so, mention the artist's attention to detail or technique in creating a realistic image. Lucian Freud's nude paintings are a good example of realism.
Impressionistic pieces will have visible brush strokes, movement, and an emphasis on light in the composition. Take a look at the paintings of Monet and Renoir, and you'll be able to recognize an impressionistic piece instantly.
If the artist has created the image using blurry brush strokes or has created a composition, like a bowl of fruit, entirely out of geometric shapes, it's safe to ooh and aah over the artist's interpretation of reality and label the technique as expressionistic. Look to Munch ("The Scream") to see what expressionism is all about.
If you're discussing a piece and secretly thinking "I could have painted this when I was 5," you're looking at Abstract Expressionism. Jackson Pollock's pieces and your 4-year-old nephew's doodles are good examples of Abstract Expressionism.
From cubism to minimalism, there are dozens more specific art movements, with many artists fitting into more than just one category, so don't sweat it if someone starts throwing around terms you've never heard before.
Once you're all out of Art History 101 vocabulary, just give your honest opinion. Whether you love it, hate it, or just don't see what the big deal is, the most important thing is that you're thinking about it and that it makes you feel something, even if it's disdain. Trust us, your art museum companions probably don't know much more than you do. 'Fess up to your limited knowledge and they'll likely breathe a sigh of relief that they're not the only ones faking thoughtful nodding while mentally writing up their grocery list.