Both NAND and NOR gates are universal in the sense that any other gate can be built from them. To build an inverter from NAND, simply connect the two inputs of the NAND together and use this junction as input of the inverter. Therefore an AND gate can be realized simply as a NAND followed by another NAND with 2 inputs tied together. This is shown in the attached figure 1.

To get an OR gate from NAND gates, we need 3 NAND gates, 2 used as inverters connected as shown in Figure 2. There is a standard procedure to convert gates to NANDs or NORs. I may explain it if requested. Thanks. @AlDmour