(As a rule of thumb older houses with plaster are 16" apart while newer houses are more likely to be 2' apart. But not always.. In some very old houses there is no standard spacing.)
In either case the lathe or the drywall is either nailed or screwed to these studs. So, you need a device to detect these fasteners.
The hardware store sells a "stud finder" (LOL! I want to see you walk in and ask for that, but it's the right name I swear.) and it's basically a device that senses these fasteners through the wall covering. (sometimes they are a simple magnet, others may be battery powered and use a hall effect sensor)
The instructions for the devices vary, but basically you slide it down the wall till you find the fasteners which means you located a stud.
OR
If you can locate one stud you can measure 16" or 2' to locate the next stud with a fairly high degree of accuracy..
OR
If you can remove the baseboard or have access to the unfinished area that's typically covered in some similar fashion at the bottom of the wall you can slide a hacksaw blade (or something else that's think and flexible) down till you hit the bottom of the studs.
Now, you come paint my boat.