As the others have covered the actual months and times you can encounter the scorpion, I'll just say that unless they just appear unexpectedly while you're walking and they suddenly attack then there isn't a whole lot to worry about with scorpions or tarantulas. They strike a threatening pose when they notice you nearby, but if you just stand still then they'll calm down again. You can approach them slowly one step at a time, they'll repeat the threatening gesture so just stand still again. Once you're close enough using this method you can simply catch them with your net.
Something to note about scorpions and tarantulas is that they only spawn in open areas without things like flowers occupying space on the ground.
Not sure whether you still needed to catch one for the museum or something or if you were just asking for general knowledge, but yeah. They sell for a decent amount at Nook's Cranny too, so it's worth getting used to capturing them for a quick payday.