This recipe by Joe Mattioli from the Got Mead? forums is the one usually recommended to any eager newbie asking what to make, and that’s because it gives you a tolerably tasty result in a fairly short time using only ingredients and supplies from your local grocery store. This process doesn’t teach you much, if anything, about things you will definitely need to know if you plan to get even slightly serious about mead as a hobby — flavour balance, nutrient management, sanitation, bottling practices, and so on — but it has a low barrier to entry in terms of cost, time, and equipment requirements.
You can find the original recipe here, where it was restored after the GotMead servers suffered a data loss. I’ve adapted it to suit my preferences for recordkeeping.
On November 3, 2016, I started a variation on this recipe. I used a wine yeast (Lalvin D-47 from my favourite local wine supply store, BosaGrape) and only the juice and zest from the specified orange. Since I have only Imperial gallon jugs on hand, which amount to 4.5 litres in volume, I scaled the recipe up. (Imperial gallons make for a decent batch size; you can get 12 half-bottles out of one.)
Disclaimer: I have personally never done this exact recipe before, because I already had some experience and supplies from winemaking when I moved on to mead, but dozens of people in meadmaking forums all over have reported that they have done it with mostly acceptable results. This recipe is intended to finish sweet, which will cover up any off flavours that might result from inexperienced handling, bitterness from the pith, or stressed yeast.