There are many ways.
For a beginner, as strength gains can be very fast -- sometimes say 5% a week for sustained periods -- it is entirely workable to add a rep per week until reaching some figure, then adding weight and building reps back up again. As noted, this shouldn't be to an extreme such as down to 2 reps.
Those who have already increased their strength greatly from their starting point are not generally going to see sustained strength increases as fast as 2-5% per week, which is what an added rep typically represents.
There are many methods.
There is a lot to be said for periodization: that is to say, not training at the same percent 1RM all the time, but in a programmed plan.
For example, if following the Wendler 5-3-1 plan, week 1 works up to 77% 1RM (if not employing the arithmetical gymnastics), week 2 works up to 81%, week 3 works up to 86%, and week 4 is a deload week.
Then next time around some modest weight is added. Or in other words, weight is added per 4 weeks, not per 1 week, but every workout is heavier than the last workout that was at the same percent 1RM.
Or another example, I used to follow a progression from Scott Warman where training cycles started at 60% 1RM for 2 sets of 9 in each exercise, and added 5% 1RM each week till ending at 2 sets of 3 at 90%. The nominal 1RM (used for calculations) would then go up for the next cycle. Again, each workout is at differing percent 1RM, and that weight is always heavier than the last time that percentage was used.
Or presently I follow a system where an Excel spreadsheet has a column (call it A) for starting 1RM's or values used for such that were correct at a point a while back, then a column B which originally was simply a copy of Column A but is allowed to be tweaked as appropriate though not to values less than in A.
There is a cell for the number of weeks into the program, the multiple of increase aimed for per week (I am using 1.008), and that increase raised to the power of the number of weeks. So for example, 10 weeks later, that cell will have the value of about 1.08 (actually 1.083 due to compounding). That actually is a very aggressive rate. Matching it is good success.
A column C then has the Column B figures multiplied by this planned strength increase, for each percent 1RM I might want to do.
I can then do any workout program, changing on the fly if need be, with weights that increase slightly with time.
Yes, this requires actually writing things down and planning, and I know that many have gotten big and strong with no writing or planning and don't want to do any. But if dealing with the question of how to add weights when strength isn't increasing as fast as 1 rep per week or 5 lb per week, then these ways which do involve planning and writing can be very useful.