How can one prepare mint for a Mojito a way that will optimally extract its flavor? Are there any other factors that are important while making the drink?
The best way I've found to get full flavor out of the mint is to infuse your liquor with it. I do this for mint juleps. Simply take a handful of mint, bruise it (you can just crush it in your hand or stick it in a bag and whack it a couple of times with a wooden spoon), and place it in your liquor of choice (white rum in this case) and leave it for a day or two. You'll need to experiment with the right amount for your drink, but I loosely pack a mason jar about half full to do bourbon.
If you want the actual leaves in your drink, then you need to make sure you muddle the mint rather than just putting it in. What you want from the mint is the oils in it, these are released better when you bruise the leaves. So just chopping and throwing it in won't work well. You actually need to crush them.
It's also important to use the lime rind in addition to the juice. And again, muddle it. The reasoning is the same. There are oils in the rind that are released during muddling that have a decidedly different flavor than just the juice.
To finish out, pick your sweetener. I like to use simple syrup, but you can also use sugar (or anything sweet, if you want to change the flavor, try a flavored syrup). And then top it up with something non-alcoholic. I particularly like sprite, but also use lemonade or sometimes just soda water. Be careful to balance the sweetener based on whatever you're adding; Sprite obviously needs less sugar added than soda water.
I prefer to muddle the mint. Muddling is simply bruising the mint with a stick.
If you are using sugar (white or cane sugar) to sweeten your Mojito instead of syrup, you can put the sugar in the bottom of the glass and bruise the mint on top of the sugar. It works well to muddle with about a shot (or half shot) of alcohol as well. Muddling gives you a fresh, clean and "uncomplicated" flavor.
Blending or chopping the mint or even over-muddling causes lots of little bits of leaf to separate and float around in the drink which is not enjoyable. Muddling lightly but enough to bruise the whole leaf without separating it into chunks has the result of maximum flavor with minimum mess.
I let the muddled mint soak in the glass along with the drink and the mint contributes over time. When you sip a Mojito, sometimes the best and brightest flavors come near the end of the glass.
If you were making batches of Mojitos you can premake a batch and let it soak a bit in advance (15 minutes is probably enough to get a close to ideal flavor). You can even strain the batch as you pour to avoid getting mint leaves and other debris in the serving glasses.
I'd avoid long term infusion unless you are ready to experiment a bit and possibly make batches you won't like. I have done deep infusions of both spearmint (rum) and peppermint (vodka) where you pour out about 1/4 of the bottle's liquid content and pack the rest with mint - then leave it sit in a dark place for 3-4 weeks (light can affect the flavor). The result is a very strong, greenish mint extract with rich bitter tea flavors. Diluting the Peppermint Vodka infusion with equal parts of normal vodka and adding some simple syrup makes a nice "Peppermint Schnapps".
An important thing to note is infusion deeply extracts flavors -- more just the mint oils and the "fresh" mint flavors you get from muddling. It will actually extra the color (chlorophyll) and have a much more leafy flavor (think tea) rather than just the cleaner light mint flavors you get with muddling. In some cases these flavors are not desirable -- think about the bitterness you can get when you over-steep tea. Some of these flavors can be reduced by using only leaves or leaf tips and avoiding stems and branches which add higher levels of alkaloids and bitterness. The only way to make those bitter flavors palatable is by diluting with uninfused liquors and water and adding sugar to mask the bitterness.
Infusions do yield interesting and rich flavors but they require experimentation and a long term view where you may be willing to prepare your alcohol for the Mojitos several weeks in advance. In my experience, they may also not yield the best desired flavor compared to simply letting fresh leaves steep for a short time.
Short term infusion as noted in another answer (1-2 days) sounds interesting but some of the fresh flavors in mint are very volatile (i.e. think of the smell immediately when you tear a mint leaf in half). These volatile flavors become a bit more muted compared to the other flavors when infusing for any length of time though, even just a day or two.
For mojitos and juleps, I like to make a mint simple syrup. Basically you add a bunch of chopped mint leaves to a 1:1 sugar/water mixture, heat it until the sugar is dissolved, take it off the heat, and let it steep for an hour or two. If it's not minty enough, just put it back on the heat for a bit and repeat. For one cup of sugar/water, I threw in ~1/2 cup of chopped leaves.
Recipe (serve over ice): . 2 Tbsp Mint Syrup . 1.5 oz white rum . 1.5 oz club soda . garnish with mint leaf
Sugar will extract the mint oils, I have found. It is very easy to put mint leaves, stripped from the stems, and mint tips with tender stems, into a plastic storage bag, tossing and rubbing the closed bag to muddle and bruise the mint. Leaving it for several hours or overnight flavors the sugar. You can then proceed with making a mojito batch by adding lime juice (fresh or a good quality bottled ...i.e. Nellie and Joe's Key West Lime Juice), letting it dissolve with a bit of rocking from time to time, rinsing the bag with some water, and straining. At serving time, add white rum and club soda.
Proportions for a batch of ~ 30 9-oz drinks: ~ 4 c trimmed mint leaves, 2 c sugar (could try 1 1/2 c), 2 c (16 oz) lime juice, 1 c water to rinse storage bag when straining. For finishing the drinks, 1.5-1.75L of rum, 2L of club soda, and garnish with fresh mint and a lime wedge squeezed to release lime oils.
as yossarian said, DEFINITELY make sure you use the lime rind. it's key. i'm not sure about infusing the liquor -- just use really fresh mint, muddle it until the sugar & syrup is all mixed well, and you'll have a great mojito. if you can, get the red-veined mint (the flavor is better). here's the recipe i've used that has served me well for many years:
2-3 ounces light rum, 1 ounce lime, 2 teaspoons sugar, Mint, Soda Water
Place sugar, a large pinch (small handful) of mint, and splash of soda water in a pint glass. Use muddler to lightly press mint and dissolve sugar until it smells of spearmint gum. Squeeze both halves of lime into the glass, leaving one hull in the mixture. Add rum, stir, and fill with ice. Top with soda water, garnish with mint sprig and serve.