"Tsuna one day comes home, greeted by a little baby mafioso who apparantly is his new home tutor. His job is to guide Tsuna into his role as the 10th Boss of the Vongola family. With the help of all his new friends and an array of special items such as the ,Dying Will Bullet, he might just be able to do it."
This is the manga's summary.
Please do watch it, it's really good. ^_^ But I have to warn you, the first 20 or so episodes aren't that good. The art isn't as awesome, and they're all just 'daily life' episodes where the characters are introduced and etc. They're sort of like fillers.
After that arc, it will start to get good (in both the art and plot) so please try to see it through. XD