To make tagliatelle, roll out fresh pasta dough with a pasta machine until it's very thin. Dust the sheet with some semolina and fold it over itself four times. Use a knife to cut approx. 1/4-in. (1/2 cm) wide strips, then dust the tagliatelle with a little semolina again and loosen with your hands so they don't stick together.
To make farfalle, roll out the dough at the thinnest level of the pasta machine and cut it into 2-in. (5 cm) wide strips with a knife. Then cut squares with a pizza wheel (or a pasta cutter if you have one). Fold them twice in the middle with your fingers to create the classic bowtie shape.
To make cavatelli, roll the pasta dough into thin strands and then cut them into small 1/4-in. (1/2 cm) thick pieces with a pastry cutter or knife. Press each piece in with a fingertip, in order to shape small, round plates.