Plateaus and Strength Training?

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I hit a plateau recently. I'm past it now, but I'm not sure why or how it happens. I'm sure it's perfectly normal for this to happen. I have maintained my daily calories and do not eat unhealthy foods (almost no processed foods...mostly fruits, veggies, fish, chicken, turkey, whole grains, and some dairy), and I've been working out regularly. I try to change up my workout so that my body experiences something new throughout the week. I have not, however, been doing a lot of strength training. We just don't have the money for gym membership right now. I did buy some hand weights and I've tried doing a few things I've researched online, but for the most part, that's not a regular part of my workouts. Maybe that's the problem?

My main question is how do you get past a plateau, or do you just wait it out? I definitely don't stop working at it, but I have to admit that it's a little discouraging when it happens.

Also, if you do strength training at home, what are some things you do? I know a Gym is going to be my best bet, but until that won't "break the bank", I'm going to have to do all my strength training at home.