I think a good habit to form is disconnecting the leads from what you are measuring before changing modes. With typical DMM test probes, this can be as simple as letting go so they break contact with whatever you were measuring.
But most DMMs have input protection for all functions, so the worst that should happen to the DMM on a typical electronics bench is you could blow a fuse (a typical DMM will have a high-current fuse around 10A and a low-current fuse around 500mA).
However, there are some DMMs that do not have a fuse for the 10A range, so that might be worth discovering now on purpose rather than later by accident. This could damage the DMM, probes or your other equipment.
A common misunderstanding among new users is how to measure current with a DMM, which is a series circuit, not parallel.
What DMM(s) do you have?