Spearmint leaf is used in many wonderful drinks. It imparts a subtle mint flavor which is quite refreshing and mixes well with a variety of base spirits. The best way to obtain spearmint leaves is to just grow it yourself. Unless you live in Arctic, you can pretty much grow spearmint anywhere. It grows like weeds and can even be used for ground cover.
I grow my plants in pots to prevent spreading. Planted in the ground, spearmint will aggressively spread which can cause problems for neighboring plants. This won't happen in a pot. You want a good size pot to allow the spearmint to do it's spreading--12 inches or larger. I use a 16 or 18 inch pot to grow a lot. You can get by with a smaller pot if you stay on top of using and pruning the spearmint leaves.
Any decent potting soil will do as spearmint doesn't need a lot of nutrients to grow. Just make sure the soil drains well. Plant as soon as it stops freezing at night and water the mint every other day or so and more often during a hot summer.
When you approach the end of your growing season, use all your remaining mint to make mint syrup to get you by till the next spring (unless you buy spearmint leaves from the store).
I have had the best luck with the actual spearmint species Mentha spicata. This is the spearmint leaf you know and love and it yields plenty of oil and aroma for your drink recipes. You will see other types of mint at the nursury such as Kentucky Colonel or Mint Julep varieties. These are decent but they never seem to pack the punch of good old Mentha spicata.
There is a dizzying variety of "flavored" mint plants that have probably been developed in a lab somewhere. These include chocolate mint, orange mint, apple mint, and many others. These plants could work well in some drinks (particularly the chocolate mint in a chocolate martini), but for your classics you will want to stick to Mentha spicata spearmint leaf.
Pick a sprig off your plant and rinse it to clean off any dirt. I usually then pick the leaves from the bottom of the spring to use in the drink. The remaining leaves at the end of the spring can be used for the garnish.
When muddling spearmint leaves you want to be gentle. If you muddle too aggressively you will end up with a bitter, vegetal tasting drink. Gentle muddling will extract the spearmint oil without ill effects.
For a mint garnish you want to slap the sprig of mint between your hands before you garnish the drink. This will release some of the spearmint oil and result in a more fragrant drink. Another trick is to cut the straw so the drinker has to nestle his nose in the spearmint garnish in order to drink.