For toning and strengthening I would guess you could just do different variations of curling, and extending your arms out and up, etc.
One way I remember using hand weights like that was in my Zumba class! We had one dance each class that used the weights. Zumba is really easy and you can kind of do your own version of it at home, it's just like easy dance aerobics. So for example, we would do a grapevine move back and forth (8 steps to the left, 8 steps to the right, back and forth) and we would hold the weights up with bent elbows (making a W shape with our arms), and then with the next step, we would extend our arms straight up, and then bring them back down to the W with the next step. We would also do deep knee bends, forwards and backwards, while pumping our arms with each bend (like a slow-motion running movement, the way your arms move when you run).
Doing things with the weights by themselves might only tone your arms, but if you combine them with another light aerobic activity like dancing, they really give you a workout! I was always way more exhausted after the weight dances than the regular ones. It just makes you exert more energy over-all, getting your heart-rate up, and makes it harder to balance and things like that.
The great thing about something like Zumba is that you can learn some moves and then use them to dance to whatever music you like! Most of the moves I learned were just silly, repetitive things, not like real dancing, but with the right music it feels really fun =)
Here's a youtube user with a bunch of Zumba videos! http://www.youtube.com/user/CocoFitness
See which ones you could integrate your hand weights with and start dancing to some of your fav anime/jpop music!