NF3 has three F atoms bonded to a central N atom, with one lone electron pair on the N. What is the shape of this molecule?

When you write the Lewis structure you see that you have three bonding pairs and one lone pair on nitrogen, the central atom.

What (a) is asking for is what is called the "electron pair geometry", which in your case is tetrahedral. As the name implies, the electron pair geometry looks only at the electron pairs, and not whether they are bonding or not. The electron pair geometry will establish what geometry the molecule can be.

Question (b) is asking for the "molecular geometry", which is trigonal pyramidal. "Trigonal pyramidal" is withing the "tetrahedral" family of electron pair geometries. The molecular geometry looks only at the shape created by the atoms which are bonded to the central atom. The N and 3 F's form a trigonal pyramid, not a tetrahedron, since there is not a fourth atom bonding at the lone pair.