VRAM can't be upgraded. But the vast majority of VRAM is used for textures. If this laptop has a 720p screen, you're never going to use more than 2GB of VRAM - just switch from high textures to medium if you start getting close to 2GB. You shouldn't be able to tell the difference at 720p.
2GB is usually enough for 1080p, except for newer titles released in the last ~3 years. And even there you can get them to work in 2GB of VRAM simply by decreasing the texture size.
All that said, a quick Google search suggests your laptop has a 820m Nvidia GPU. That's a very low-end GPU, which is actually slower than the integrated graphics on newer CPUs. If you want better gaming performance, you'd be much better off buying a new laptop. I'd...