If helps any for you when looking into how to do this, the usual terms for this are 'alpha blending' or '
alpha compositing'. Technically speaking, alpha blending is a particular type of alpha compositing, but you'll sometimes see it used for other types of alpha compositing. It is related to the broader topic of image compositing, as well as loosely related to the issue of texturing.
As Ben said, this is something you'd have to do in software, at least for a generic video framebuffer. While the current generation of GPUs used in PCs do have hardware compositing, you would need a hardware-specific driver to use that, and you'd want to have a software method as a fallback, so it makes more sense for most hobby OS devs to stick to that.
There are a number of different algorithms for different types of alpha compositing, and each has uses in different situations.
Can you give us some idea of what you are trying to accomplish? I think is smell an
XY problem in this, so more context is definitely called for.