Make sure you’re doing a variety of exercises. Bench press, for example, primarily work your pecs, but they also use a variety of other muscle groups-- the delts, for one. If you’re focusing on exercises that isolate certain muscle groups (I think curls, for instance, work only your biceps), you may not be building the surrounding muscle enough to see a general strength increase.
Even so, if you were just working on curls, you should have seen a slight strength increase in working out consistently for a month. Are your muscles tired the next day? In my experience, 3 sets of 10 is enough to build strength, but if it’s not working for you then try increasing the weight, as others have suggested. One type I was fond of was a set of 10, increasing 2.5 kilos (or whatever it takes), doing a set of 8, increasing the weight, and doing a set of 6.
When I was lifting, I seemed to remember my arms being tired from immediately after my workout to about an hour afterwards, and then the next day they were actually sore (eg painful to use in my daily routine, tender to the touch). When you lift to increase strength, you’re creating tiny tears in the muscle tissue, which fills in with more muscle (hence why you need the protein), so they should hurt a little bit.
There are other things you can do (supersets and such), but I would work on increasing overall strength by doing exercises that target large muscle groups (bench, lat pulldown, military, incline bench-- for upper, squat, deadlift, lunges-- for lower), and it should start getting you where you want to be.