The fragile electronics within voltage detectors and testers will usually be protected by a hard casing, which means they can usually be stored in a toolbox.
For devices with exposed metal probes (voltage testers), it is beneficial to cover them when not in use, to avoid dirt damaging the workings. Often, caps will be provided for the probes; if they are not, use something non-conductive to cover them (plastic or cloth). Take a little extra care with the cables, and try not to get them too tangled.
Voltage detectors and testers do not require any deep cleaning – just wipe them down with a damp (not wet) cloth every now and again.It may be helpful to ensure any probes or screens are kept clean, again using a cloth, to ensure you get accurate results. There are specialised cleaning wipes available for these.
Ensure your devices are fully functioning before each use. Change batteries and fuses when necessary and consider removing the batteries if the tool will not be needed for an extended period of time.