Wash your lemons well, and then using a sharp paring knife or a vegetable peeler, peel off just the outer yellow part of the rind. Try to get as little of the white part as possible.
Dump the peels and vodka into your container.
Wait a while (like, 3-4 weeks). Shake the container whenever you think of it. Also, juice those peeled lemons and freeze the juice into cubes for later cocktail use.
Make the syrup and final liqueur
To make the syrup, just combine the sugar and water in a saucepan and heat on medium high until it boils. Let it gently bubble for 5 minutes, then remove from the heat and let it come to room temp.
While the syrup cools, strain the lemon peels out of the vodka infusion. Then, strain it all again through a fine mesh sieve. You can even line the sieve with cheesecloth to make sure you get any little lemon bits out.
When the infusion is strained and the syrup is cool, combine the two in a large container and mix well. If you used Everclear or another high-proof base, it might turn cloudy at this point, which is totally normal.
Congrats! You have limoncello! Now use a funnel to put it into those fancy tall limoncello bottles. You can maybe give one away as a gift, but if you'd rather hoard them all, that's cool with me.
You can store at room temp, but many people keep it in the fridge (or freezer if you used Everclear, just for an extra cold drink).
Notes
Instead of vodka, you can also use Everclear or grain alcohol. This will reduce the infusion time, but you'll need to increase the amount of syrup you add. Using this higher-proof spirit will also likely cause your limoncello to become cloudy when you add the syrup, which doesn't affect the taste at all.