Yes indeed, it is definitely something you can easily do. If you deadhead your pansies to keep them flowering you won't get many seeds, only from those which you have somehow overlooked, but if you let the flowers die naturally a certain amount will turn to seed heads, depending on whether or not they have been pollinated by some insect. When these seedheads change colour, but before they split into three parts, in each of which will be a little bundle of seeds, easily visible, take the seedhead inside and place it in a window in a bowl or on a saucer. When the seedhead splits you can shake the seeds into a container, and place them in foil to store in a cool place for next spring, or sow now in a sheltered area outside. I have seen it written that they need dark to germinate, but not knowing this, I have sown viola and pansy seeds in an open tub and they have germinated no problem.
The only thing to be aware of is that the seeds may not produce seedlings identical to their parents, however, a bedding viola which ran to seed in my garden last year has produced several seedlings around the garden naturally which all are very similar to the parent. It's just something that you can't depend on. Some of the seedlings might even revert to the wild form of pansy or close to that. On the other hand, you might come up with a wonderful new variety of pansy, from which you can take cuttings in future years.