When I am setting up for a multiple fan test, do I use a router or a switch and how do I configure the DM32 gauges and my control computer (settings and wiring)?.

Routers and switches are different kinds of networking equipment, and are not interchangeable.    

A switch will for the most part just pass the traffic through. Switches can be used for multiplexing so you can get multiple inputs onto one output.  They can also be used as signal boosters so you can extend the length of your data connection.

A router will dynamically generate IP addresses for devices connected to it.  The router will also multiplex and boost signal.

When networking, it is important to understand what piece of equipment is in charge of generating the IP address for each device.  If there is a router anywhere in the network to which you are connecting gauges, that router will provide the IP addresses. 

Gauges connected to a network containing a router must be set to DHCP for their IP address generation, because these gauges expect the router to tell them what IP address they will use.  You have to set DHCP on the gauge itself (network settings screen>>"Mode") then the gauge will wait for the router to tell it what IP address to use. 

Gauges connected to a network containing only switches must be set to Static and have a UNIQUE IP address entered, because the gauge itself will need to know its IP address in advance of connecting to the network.  You have to set both of these things yourself on each gauge (network settings screen>>"Mode" and "IP Address"). 

For ease of configuration, I would use one router connected to the control computer and set all the gauges to DHCP.  I then use switches if I need to gang gauges together at a location.  For instance if we have two banks of fans at separate locations in the building, I would use a switch at each bank, and then feed one cable from each bank to the router.

It is best to use the computer you are taking to the jobsite, and use the network equipment you are taking to the jobsite to set up and test your network before you go. 

Most computers are configured so that they will operate either on a network with a router (DHCP mode), or on a network where devices need to know their own IP address (Static mode) without the user having to change any settings on the computer.  Be careful when plugging the devices into ports on a router.  Most ports will be labeled for LAN and one will be labeled differently (WAN or Internet).  Be sure to plug your control computer and devices only into LAN ports, never the Internet/WAN ports or there may be routing issues.