The tail fin looks as though it has a chunk missing. This could be because it has been caught on something and torn off, or because the fish has been biting its own tail though boredom in the shop or because it has finrot. Keep an eye on it - damage or fin nipping will heal and the fin will regrow. Finrot may get worse. Lots of water changes will help prevent finrot developing further.
The fish looks like a he not a she. The pelvic fins - those long dangly things under the head - are too long for a female. But the way to know for sure, and to see which type the fish is, is to place a mirror by the tank where the fish can see its refection. A betta, male or female, will usually flare out its fins when it sees what it thinks is a rival. With a female, the gills stick out only at the side of the head while with a male the gills stick out all the way under the head as well making it look like a beard.
When the fins are flared out, you'll be able to see them in their entirety. Yours looks to have quite a lot of finnage: if the edges of the tail are 180 degrees apart, it's a half moon; if they are not quite 180 deg apart, it's a super delta; if the edges are more than 180 deg its an over half moon.
It's hard to tell from the photo, but if the scales are very thick it's a dragonscale, if they are like normal fish scales, there isn't a term for that.
As for tips:
How did you cycle the tank? So many people think that letting the tank just run is cycling so I like to make sure. Unless you added ammonia until certain targets were reached and/or added a bacterial starter, the tank will not be cycled. But even if you did this,I would test the tank water for ammonia and nitrite for a few days to make sure they stay at zero. Any time either is not zero, do a water change.
As I said earlier, keep a close eye on the edge of that missing bit in the tail. Even if ammonia & nitrite stay at zero it is worth doing a water change every couple of days till you see signs of regrowth.
Once you are sure ammonia & nitrite are staying at zero and the tail fin is obviously healing, do a water change of at least 50% every week. Suck up any debris on the sand at the same time.
Be careful not to over feed. Bettas are pigs and yours will soon recognise you as the food giver and will beg for food. Don't give in!
Have the light on a timer, if you've not already done that. All fish tanks should have the lights on at the same time of day every day, and for the same length of time. Make sure that the room is in daylight or the room light is on for at least half an hour before the tank light turns on and half an hour after the tank lights turn off. This is a sort of dawn and dusk period for the fish as their eyes take around 30 minutes to adjust to the tank lights turning on and off.
I am sure other members will have more tips for you
