As SevenSidedDie points out, in DnD it is generally easy for a spellcaster to hide the fact they are spellcaster if they wish.
With that said, when they aren't hiding the fact, then the hints will often be fairly obvious. Wizards will often have pouches with spell components and if travelling in a group may be the only one without armor in an otherwise heavily armed and armored groups. Clerics will generally be proud of their faith and likely have the holy symbol worn openly and may even decorate their equipment with other signs of their faith. Of course, it is possible for someone wanting to seem powerful to masquerade by wearing symbols of faith or pouches of components even if they can't even cast a cantrip. But it is still a decent indicator.
Now, if you want to look outside of DnD for somparison when making your own game, it is a fairly common trope for certain types of magic users to be able to see auras and for those auras to display signs of magic use. Shadowrun has this well developed and Vampire: The masquerade used a similar system as a power under the Auspex Tree.
It would also be reasonable for use of magic to have side effects that show its presence on the user. The expanded universe for Star Wars has a concept of "Dark Side Corruption" where extended use of the dark side will physically disfigure the user. While certainly not magic users per say, the mentats in the Dune series tended to be addicted to Sapho which would stain their lips purple.
It might also be the case that very powerful magic users would radiate the energy they are most attached to. A fire wizard might always be physically hot and possibly glowing. Mage: The Ascension in its high level supplement discusses this happening for mages that reach very high ranks in a sphere, especially those that become "exemplars".