First, for youtube, right-click -> Stats for nerds. Watch the "Dropped frames" counter, with hw acceleration it usually stays close to zero("-").
For youtube&everything-else, you got two major tools:
1. CPU usage, just watch it, if you don't see spikes while playing video, you're good(on quad core 4th gen Intel core I get around 7% increase in load for HW-accelerated youtube 1080p video).
2. Even better: Tools like GPU-Z[0] have "Video Engine Load" meters for some GPUs(e.g. Nvidia GTX), where you can see if the GPU dedicated accelerator is working(and how much). For other GPU-Z(e.g. Intel HD) you can monitor the general "GPU Load", you will see an increase there as instead.
P.S. In addition to the above, in some browsers(in chrome, via chrome://flags) & media players you can disable the hardware acceleration support and observe the results using the tools I've mentioned.
For youtube&everything-else, you got two major tools: 1. CPU usage, just watch it, if you don't see spikes while playing video, you're good(on quad core 4th gen Intel core I get around 7% increase in load for HW-accelerated youtube 1080p video). 2. Even better: Tools like GPU-Z[0] have "Video Engine Load" meters for some GPUs(e.g. Nvidia GTX), where you can see if the GPU dedicated accelerator is working(and how much). For other GPU-Z(e.g. Intel HD) you can monitor the general "GPU Load", you will see an increase there as instead.
[0] http://www.techpowerup.com/gpuz/
P.S. In addition to the above, in some browsers(in chrome, via chrome://flags) & media players you can disable the hardware acceleration support and observe the results using the tools I've mentioned.