It looks like mine is different from what I'm finding online. Okay, for one:
Peel a cucumber. Slice into quarter to half inch rounds.
Depending on how much cucumbery taste you want, put a quarter to one half of a round in the bottom of a cocktail shaker.
If you have a smooth muddler, you might want to add just a bit of salt to help the muddling. Mine has ridges, so I don't unless I'm in the mood.
Smash/muddle that cucumber.
Add 3 oz of gin.
Depending on how dry you like your martininis in general, add up to 1/4 tsp of dry vermouth. I like dry, so I just whisper the word "vermouth" over the shaker.
Strain into martini glass. Garnish with one of the cucumber rounds or cherry tomato, or even just put a chunk of cucumber in the bottom of the glass.
*I know martini purists cringe at shaken martinis, but I didn't know what else to call this drink.