I use a Squeezo strainer, so I heat the tomatoes to soften them first. The strainer removes the seeds and skins. However, if you've got something like a Vitamix (powerful blender) you could simply puree them, skins, seeds and all... the texture wouldn't be as smooth, though.

But if you're doing this the "old fashioned way" I'd probably peel them and seed them... or heat them through and put them through a food mill.

Summerthyme