These little roses sold in grocery stores are meant to be disposable. Once they're done blooming you just toss them out like you would a bouquet of spent cut flowers. However, with proper care they can be enjoyed for many years. All in all yours really doesn't look too bad.
It's probably too cold yet in Hungary to plant out yet so for right now you need to take off the pretty basket and check the bottom of the pot for drainage holes. Roses like a good amount of water but they hate to have wet roots. So you need a pot that allows you to soak the soil but have all the excess water drain away. So you do not want any kind of cover or tray on the bottom of the pot that holds the water against the bottom of the pot so it can't drain away. Prune off all the dead blooms and any leaves that are shriveled. Keep it in the very sunniest place you can find in your home. As Luis said, it needs as much sun as possible. Then as Daisy indicated, get it outside, and planted in the ground if possible, as soon as you can plant outside in your area. With good care you should be able to enjoy it for many years to come!
