In the 2017 TV Series, Broomsticks have a cloaking spell so that non-magical people cannot see the Broom and it's rider in flight.
Flying a Broomstick
To ride a broom, you first order the broom to hover, and it hovers lengthways above the ground. Then you sit on it, give it a sharp tap, and away you fly. Once in the air you can make the broom do almost anything by saying, ‘Right! Left! Stop! Down a bit!’ and so on. The difficult part is balancing; if you lean a little too far to one side you could easily overbalance, in which case you would either fall off or find yourself hanging upside-down and then you would just have to hold on with your skirt over your head until a friend came to your rescue.
It took Mildred several weeks of falling off and crashing before she could ride her broomstick reasonably well, and even then she isn't that good at it.
BehaviourWhen broomsticks are near the water their magic powers are far less efficient- they don’t work so brilliantly when their magic is damp. For this reason it is difficult to keep a broomstick stable directly above water. However, if the broomstick is hovering a good few feet above the waves, it will be strong enough to pull you along behind on water-skis, a sport called Broomstick water-skiing.
Magic broomsticks that are owned by one person for a very long time (Miss Hardbroom had hers for twenty-five years) develop a strange kind of intuition about their owners. In the same way that a dog will stand at the front door and wag its tail when its master is getting off a bus at the end of the street, a broomstick can sometimes sense that its owner is nearby, and if the owner is in trouble, that sense is even more acute. In such cases a broomstick is able to locate and fly to its owner. Miss Hardbroom's broomstick does this in The Worst Witch All at Sea (book), and The Dragon's Hoard (TV)
In the 1998 TV series, students at Cackle's Academy must pass the Broomstick Aptitude Test in their first term in order to continue at the Academy. Mildred only just passes the test, and Sybil Hallow also struggled, with Ethel being asked to tutor her sister. Henrietta Hubble passed her Broomstick Aptitude Test, but her friend Cressie needed some help as she wasn't feeling confident.
In the books and 2017 TV Series, the Broomstick Proficiency Test (BPT) is taken outside of school, prior to or during a witch's education. Maud took her Broomstick Proficiency Test prior to starting at Cackle's, and her parents bought her her first broomstick for passing the test. Mildred took her Broomstick Proficiency Test in the summer holidays between her second and third year, and also received a new broom from her mother, though it was broken shortly into the term, ending up with tape around it like her first one.