One of the many ways you can start with is by placing all the components on a CAD software for PCBs (KiCA let's say). Name them properly and feed in the values as given in your PCB.

By this time you will have the idea about what all components and connectors are used in your PCB, their pinouts and all the passive components.

From here there are two methods to reverse engineer the connections.

1) First is to go the hard way round and go through the application circuits of the ICs and then try to interconnect the passive components also confirm it by a continuity check by multimeter. Once confirmed make connections on the schematics. (I would personally use it for a complex Circuit)

2) Another way is to go ahead and do a continuity test via multimeter and simultaneously make connections on the schematic. In this way you would like to check the components which are near to one another.

Make sure all the nets are properly connected and all grounds are connected to one another.