I'm sorry to hear about your little guy =(
I can give you the basics of what I know.. some things you will have to decide based upon your new guy's personality.
Some say you need a tank 2.5g and bigger, but in reality they can live happily in a tank of 1g (but bigger is better, as well as it is hard to heat a 1g vs. anything larger). Some tanks are cheap, you can go the kritter keeper route, mediums at Petco are $8, and are roughly 2 gals, etc. As long as you do the proper water changes, the size doesn't matter whether it's a 1 or 55g.
For anything under 5g, without
a filter you will want to be doing 1 50% and 1 100% water change per week. With
a filter you will want to do 1 50% per week, as well as siphoning the substrate every other week or so by either a siphon or stir and dip (with a cup) to remove debris and waste from the bottom (do this in place of 50%)
For 5 - 10g unfiltered
1 50% per week with 1 100% per month. Filtered
30-50% per week, along with regular siphoning.
Always dose the full amount of water conditioner, regardless how much water you replace.
When doing water changes with fish out (keep the cup he comes in as you can use that to scoop him out of the water and hold him. Also for emergencies as a QT cup), make sure to acclimate him properly to both temp and chemistry of the tank. Such as float the cup for 20-30 mins, every so often taking out some of the water from the cup and replacing it with tank water (a turkey baster can make this easier).
Filters, it's your choice. Bettas don't need an air supply other then surface air. You just would have a extra water change per week without one. With a filter you will want to set it on it's lowest setting, or baffle it by either using an aquarium sponge in the outflow (kept in by a rubber band) or you can use a plastic bottle
to baffle it. Bettas need little to no current of water as it can stress them out, and cause drag on their long fins that can result in excess stress, tail biting.
Bettas need it to be warm. 78-82*F is preferred, so unless living in a tropical climate, you should always have a heater. Not just for the warmth, but for the stability of the temp as they can not tolerate fluxes in temps. You can buy mini heaters for smaller tanks, best to get one with a thermostat that you can set yourself. If you have to get a preset, just be aware that sometimes it can go too warm and harm your fish, or it may not get warm enough. Some people never have issues with them.. but it is something you should keep an eye on.
Aquarium Salt, Epsom Salt (you purchase at any pharmacy in places such as Walmart), and Stress Coat is always good to have on hand in case of emergencies. Do not add in Aquarium Salt for plain water changes, it should be used strictly for emergencies/healing only.
Decorations should be silk. Wide/broad leaf plants are the best, anything that does not have sharp edges or points as they can rip the fins. Think of the fins as tissue paper and can easily tear on rough surfaces. Substrate is your choice, but any dyed gravel should be soaked for a few days (replacing water often) to remove excess dye that can leech into the tank. Males tend to really love caves of sorts, whether it's a decorative cave, or a coffee cup half buried. They tend to need medium to heavily planted tanks.
They do good with a variety in their diet, but some bettas are picky.
Pellets should be the main staple in their diet. I suggest 4-6 pellets a day, spread between 2-3 meals. If they are "mini/micro" then 8-10 a day would be good. If your betta is very active then I would feed on the higher end of the numbers, if he is real mellow, then the lower end as to not over feed.
Flakes are iffy.. they should be betta flakes, and fed sparingly. They can bloat and cause coloration in the tank if not taken out immediately.
Frozen foods such as blood worms, daphnia, misquito larvae, brine shrimp are very good for them. You can easily replace a few meals a week with frozen, alternating between frozen and pellets. Cut off a tiny bit from the frozen chunk, defrost in tank water and feed 2-3 of the frozen food per meal.
Freeze dried should be used as a snack, 1-2 times a week instead of a meal. Make sure you soak any in tank water prior to feeding as it can expand in the stomach and has potential to bloat. It has a good % of the good stuff, but it lacks other nutrients needed, reason why it's best that it's not the staple of the diet.
Depending upon tank size, your betta may or may not be good with other fish. Should never get multiple fish for a tank under 5g, and at 5g it's best to get shrimp or a snail or dwarf african frog rather then another fish. This thread
will help in stocking.
Make sure there is a cover for your tank as bettas will jump, and they do need a day/night schedule just as us to get the proper rest/sleep.
Males cannot be placed together without a divider, females cannot live with males without a divider. Females living together is a sorority, and need a larger tank among other requirements, which is an iffy balance as it is. Should not be undertaken without much research.
Think that is about it.. good luck!