Sure, there are different ways to get into winemaking and develop an understanding of the basics of the process but for the frugal I would suggest this.
Go to the store and buy a Carlo Rossi 4L wine jug--$10--it costs about only a bit more than buying a 1 gallon wine carboy and has a better shape, plus it comes full of 4L of crummy wine. Probably go with the generic red or white because their version of more serious wines is a bit wanting.
Get your hands on an airlock, a bung to fit it, a ~5ft length of of food grade plastic tubing, and either potassium metabisulfite-sodium metabisulfite(basically the same thing).
Mix the 2 OZ of sulfite with 1 gallon of water- this is a sanitizing solution you will use throughout the process. Before you begin you should rinse all equipment very well with this solution.
Follow this recipe for Joe Mattioli's Ancient Orange Mead (JOAM).
Joe skips a step for killing wild yeast you will have to pick up later but it shouldn't really matter much in this situation and once you get the feel for the whole process after this it wont be a big deal to add in for your next batch
The only adjustment I would make to Joe's recipe is that you zest the oranges and add the zest and the juice while keeping the pith out.
"1 gallon batch
* 3 1/2 lbs Clover or your choice honey or blend (will finish sweet)
* 1 Large orange (later cut in eights or smaller rind and all)
* 1 small handful of raisins (25 if you count but more or less ok)
* 1 stick of cinnamon
* 1 whole clove ( or 2 if you like - these are potent critters)
* optional (a pinch of nutmeg and allspice )( very small )
* 1 teaspoon of bread yeast ( now don't get holy on me--- after all this is an ancient mead and that's all we had back then)
* Balance water to one gallon
Process:
Use a clean 1 gallon carboy
Dissolve honey in some warm water and put in carboy
Wash orange well to remove any pesticides and slice in eights --add orange (you can push em through opening big boy -- rinds included -- its ok for this mead -- take my word for it -- ignore the experts)
Put in raisins, clove, cinnamon stick, any optional ingredients and fill to 3 inches from the top with cold water. ( need room for some foam -- you can top off with more water after the first few day frenzy)
Shake the heck out of the jug with top on, of course. This is your sophisticated aeration process.
When at room temperature in your kitchen. Put in 1 teaspoon of bread yeast. ( No you don't have to rehydrate it first-- the ancients didn't even have that word in their vocabulary-- just put it in and give it a gentle swirl or not)( the yeast can fight for their own territory)
Install water airlock. Put in dark place. It will start working immediately or in an hour. (Don't use grandma's bread yeast she bought years before she passed away in the 90's)( Wait 3 hours before you panic or call me) After major foaming stops in a few days add some water and then keep your hands off of it. (Don't shake it! Don't mess with them yeastees! Let them alone except its okay to open your cabinet to smell every once in a while.
Racking --- Don't you dare
additional feeding --- NO NO
More stirring or shaking -- Your not listening, don't touch
After 2 months and maybe a few days it will slow down to a stop and clear all by itself. (How about that) (You are not so important after all) Then you can put a hose in with a small cloth filter on the end into the clear part and siphon off the golden nectar. If you wait long enough even the oranges will sink to the bottom but I never waited that long. If it is clear it is ready. You don't need a cold basement. It does better in a kitchen in the dark. (like in a cabinet) likes a little heat (70-80). If it didn't work out... you screwed up and didn't read my instructions (or used grandma's bread yeast she bought years before she passed away) . If it didn't work out then take up another hobby. Mead is not for you. It is too complicated.
If you were successful, which I am 99% certain you will be, then enjoy your mead. When you get ready to make a different mead you will probably have to unlearn some of these practices I have taught you, but hey--- This recipe and procedure works with these ingredients so don't knock it. It was your first mead. It was my tenth. Sometimes, even the experts can forget all they know and make a good ancient mead."
Thats what you should do for your first time. Kits tend to be way too expensive and make a large amount which you will probably screw up since it is your first attempt. I also made a kit (well semi-kit) my first time and ended up with 5 gallons of terrible 18% abv hobo hooch. JOAM was my next attempt and worked out far better. It makes a sweetish, orange mead and since the recipe is so explicit it allows you to skip over issues of sulfiting, measuring sugar, racking, etc. while you figure out how to just make a wine come into existence.