Sure. I started out making wine with wine kits. (like Wine Expert etc) Then I started ordering grapes and crushed them and made it. If you ever start making wine, kits is a great place to start and learn before buying grapes.
Anyhow, I make it six gallons (about 30 bottles) at a time in glass carboys. I know people who make entire barrels (about 60 gallons, but that's way out of my wheel house)
Well, I ferment in a food grade bucket or 10 gallon food grade plastic trashcan, then I age it in glass carboys. Here is white and a red in the fermentation process. The bag you see in the red is basically a cheese cloth bag with the grape skins inside of it to help add tannins to the wine.
Once they are done with primary (or heavy) fermentation (usually about a week) I remove the skins and transfer it to a glass carboy and add oak chips, cubes, or staffs if I want an oaked wine. Normally a barrel would oak it for me, but barrels are too much maintenance and generally to large for what I do. They do have smaller barrels, but carboys and small oak cubes way is so much easier for me. I usually remove the oak after a week or two. (don't want to over oak the wine)
Here is a picture of some of my wines aging in a glass carboys in a dark closet.
I generally let the whites age about 9 months to a year in the carboy, then bottle them. I usually let it age in the bottle at least another 3-6 months before opening one.
The reds, I tend to bottle after a year to 1.5 years. I try not to really drink any of them until they reach at least two years old. Time makes a real difference with wine. I've opened a red at one year, 1.5 years, and two years. and the wine may taste awful at 1 year, but taste like a $25 wine at two years.
A lot of home winemakers just bottle in used bottles or even new bottles, but just put a hand written label on it. I tend to go all out because I give some of it away as gifts and prefer for them to look good. Well, that and I'm a perfectionist.
Here are a few of my bottled wines.
My 2016 Zinfandel (it's in the carboy picture too)
An off-dry Riesling I made.
The Riesling again, with a Dragon's Blood (strawberry, raspberry, blueberry, blackberry wine), along with a Pineapple, Mango, Lime wine.
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A Shiraz I made with grapes sourced from Barossa Valley, Australia. Yes, that is Tyrion Lanister on the bottle hah. I named the wine The Imp's Delight which was a quote he said in the books / show.
This is a smaller batch fruit wine in the making that I made for my GF's friends. It's Pineapple, Mango, Lime wine. It turned out way way better than I expected.