Well first things first. What brand of vermouth? Were they already opened and when? What else do you have to work with? Vermouth is an essential ingredient, but you have to treat it with a bit of care. It's a fortified wine and has a shelf life of around 3 months, there is some debate as to whether refrigeration prolongs shelf life, but I do it anyway to be safe.
You can take that basic recipe for a Manhattan and vary the ratios a bit. I like 2 1/2 oz spirit to 3/4 oz vermouth with two dashes bitters. Rye in place of bourbon is a great Manhattan whereas scotch will make a Rob Roy. After that we're going to start needing some less commonly stocked stuff. Sweet vermouth pairs really well with campari to create a trio of excellent drinks - the Americano, Negroni, and Boulevardier. Then there are the classics like a blood and sand or a Vancouver, which calling for cherry herring and old Tom gin/ Benedictine respectively aren't likely to be an easy make for the typical home bar. Nevertheless there are a couple drinks that use pretty common stuff:
The Derby:
1 oz bourbon
1/2 oz sweet vermouth
1/2 oz orange Curacao
3/4 oz fresh lime juice
Shake. Strain. Garnish with a mint leaf.
Palm Beach Special:
2 1/2 oz gin
3/4 oz grapefruit juice
1/2 oz sweet vermouth
Shake. Strain.
Park Avenue
2 oz gin
3/4 oz sweet vermouth
3/4 oz pineapple juice
2 splashes orange Curacao
Shake. Strain.
Comedy option: the groundhog day - sweet vermouth on the rocks with a lemon twist.