Since your family bought it as a gift you should direct them to this site and show them all that's involved in caring for one. You need to acquire the following:
1) Food source. Actually bettas can go weeks without food, but that doesn't mean they should. A good quality pellet has the first three ingredients proteins. Wheat based pellets are common and they are poorer nutrition and can lead to constipation. Some bettas handle them better than others. My favorite pellet, personally, is New Life Spectrum Betta. They can be found at Petco. Petco has a NLS foods area and they may be there but at my store they can be found separately wtih the rest of the betta food. You can feed 5-8 of these a day split into two meals. Your betta will also need one fast day a week. Omega One Betta Buffet are also better quality pellets. These are larger and feeding 3-4 split up would be a good start on these. Some feed one or two more. Just watch that he's pooping regularly, and know the more you feed the more water changes you'll need to combat the ammonia build up. Whatever is left in the food container should be thrown away and replaced at least every 12 months. I replace every 6.
2) Something at least 2 gallons. Petco has some cheap glass rectangular aquariums between $10-$15. They have 2.5, 5 and 10 gallons. They also have some "kits" which run $20-$50. Your betta does not need a filter, although if you use one in a 5g+ it can make water changes and maintenance a lot easier. If you choose to filter the tank, I suggest adding a prefilter sponge to the intake tube as they can be sucked into the tube and severely hurt at best.
You’ll want some kind of lid as bettas are jumpers. Pet stores sell lids, and some kits come with them. You can also make your own simply with common seran wrap. Make sure to leave a slit in the back for air to get in as bettas are air breathers.
You don't need gravel unless again you have a larger one you're cycling. In fact leaving the bottom bare will allow you to help with ammonia build up. You can get a cheap plastic turkey baster from the baking section of your grocery store and use it to suck the poo off the bottom on a daily basis.
General rule of thumb, anything you use for your tank should only be used in your tank, and it should never have or be cleaned with soap or other such chems.
3) A good dechlorinator to treat water during water changes. My personal one of choice is Prime because it is inexpensive and it renders ammonia harmless in ways most other ones don’t. Petco and Petsmart should carry this. To help heal torn or damaged fins (you noted he’s ragged) API Stress Coat Plus can be used (with or in addition to Prime) at 1 ml per 1 gallon. Water changes are outlined here: http://www.bettafish.com/showthread.php?t=66595
For a 2 gallon 2 water changes a week – one 50% and one 100% should be okay. 5 gallon one 100% (uncycled/filtered) and if you choose to cycle a fully established/cycled tank (cycling will take 3-8 weeks) will require one 20-50% change a week.
While you are changing the tank you can use a smaller container (a lot of people like myself use a plastic solo cup) to contain the fish and then I wrap the fish in a towl to try to maintain heat in the cup. You can prepare the water ahead of time by filling gallon water jugs or various size buckets and letting them sit in the same room he’s in at least over night. Make sure to add dechlorinator at this point too. To acclimate to the large water change, float his cup in the newly changed tank water. Add a couple tablespoons of the tank water into his cup every ten minutes for an hour or so and then dump him in – trying to keep as little of the cup water from entering the clean tank as possible. If you don’t want to let the water sit, or you are using a heater then you need to use a thermometer under the running tap to match the temperature of the new water to the temperature of the tank. Temp swings during water changes can cause shock.
4) A heater and an in tank glass thermometer to monitor temps. Bettas are tropical fish and while they can tolerate room temps in the 70s for short time, it is hard on them. It will weaken their immune system and eventually they will become sick. Although it’s more expensive, it’s best to get a good quality adjustable heater as the preset ones tend to overheat the water, fail and can fry fish. At the very least watch the internal thermometer carefully to make sure temps are reasonable and stable. 76-82 is ok. 78-80 is ideal. 25w is good for a 2.5g, 50w for a 5 gallon and 50-100w for a 10 gallon. Aqueon Pro (not the normal line which are subpar), Jagar, and Marineland Visitherm are some of my favorites.
5) At least a couple of soft plants (silk is preferred but some plastic is okay.. test for this is dragging nylons/pantyhose across the plants and ornaments and if they snag it’s too rough) and a little place for him to hide. Even a ceramic coffee mug is great for this- but again nothing that could be contaminated with soap or leaching coffee into the tank. Small terracotta pots are popular as well, but make sure to plug the hole in the bottom as it’s too small for bettas and they are curious. They will try to swim through and injure themselves. You can close it up with silicon aquarium sealant, or stuffing it with a piece of sponge or something like that.
If you’re worried about the fins the stress coat and also aquarium salt (not marine salt and can be had at the pet store) at 1 tsp per gallon predissovled can be added to the tank. Any time you make a water change you will need to add back as much salt as water you took out.. so If you have a 5 gallon and you took out 2.5g for a water change you put 2.5tsp back in. Only treat with salt for up to 10 days.
If you’re worried about his condition, photos would be helpful.