Mincing garlic isn't difficult, but if all you have is a knife, this method from Cook's Illustrated is easy and produces a fine, smooth paste with no overwhelming chunks of garlic in the mix. Photo by Cook's Illustrated.
You already know that how you mince garlic makes a huge difference in flavour, so we'll put aside the garlic press and the always-efficient microplane rasp grater and stick to a single, simple blade. You'll need a little salt, too. Once you peel the garlic, chop it into smaller pieces and then use a two-handed rocking motion to dice up those pieces into super small chunks. Normally this might be where you'd stop, but grab a pinch of salt and sprinkle it over the garlic chunks.
This is where the magic happens. Cook's Illustrated notes that the coarse grains of salt (preferably Kosher salt) helps the garlic break down faster, and keeps the garlic from sticking to your knife. Now, keep chopping, but alternate with a scraping motion using the flat of your knife against your cutting board. Press and drag the flat of the knife across the garlic to create a smooth paste. Then rock the knife across the paste to break down the chunks, and repeat.
After a few passes, you'll have a smooth garlic paste that's ready to cook with. It takes a little practice, but once you've mastered it, you can mince a large amount of garlic quicker this way than using a press or grater to do the same. Hit the link below to see more photos of the process.
How to Mince Garlic [Cook's Illustrated]