Don't insert a disk into an old floppy drive without first inspecting it for dust because it's rather easy for a single piece of dust to scratch the magnetic coating and render the disk unreadable. Heads can be cleaned with alcohol and a q-tip. The heads are typically moved by a steel band, which runs with no lubrication and tends to be maintenance-free, but many old drives used either a lead screw positioner or a plastic disk with a spiral guide groove, and too much dust or old hardened grease can cause poor head alignment.
Place black electrical tape over the 1/4" notch on the side of the disk jacket, to prevent the disk from being written over. It is very easy to accidentally overwrite a disk by plugging the controller ribbon cable backwards, and you cannot trust any connector key to prevent this. The tape must be black and opaque because the write-protect sensor is usually an infrared optical device that will not work with any kind of transparent or even translucent tape, as 3M learned when it had to issue a recall for some 5.25" floppy disks.
5.25" drives often have a removable termination resistor pack that must be installed or else the computer will not be able to communicate with the drive. Only one terminator pack must be installed per ribbon the cable, except in the case of some newer (mid 1980s) 5.25" drives with high resistance terminators (usually soldered in place).
Perhaps most 5.25" drives support both 1.2M and 360K formats, and they tend to have many jumper settings. There are settings for the drive number (select for second drive, meaning #1 if the numbering is 0-3, or #2 if it's 1-4), Drive Select signal (either by Select signal or Motor_On signal), RPM (360 or 300 -- doesn't matter for just reading disks), and pin 34, which may be set to indicate Ready status, Disk Changed status, or left unused. Choose DC since Ready causes errors. 360K drives don't use pin 34, but not using it can make DOS fail to detect when a new disk is inserted (read up on the CONFIG.SYS command DRIVPARM and its '/C' parameter, or just hit CTRL-C to tell DOS that the disk has been changed).