Mild dry skin can feel tight and itchy, and you might notice flaking, particularly when wearing foundation. In more extreme cases, skin can become red and very painful, sometimes cracking and bleeding. If you encounter the latter, get yourself to your GP, as this can be caused by eczema or psoriasis and should be treated by a professional.
If you have dry skin, you'll probably notice that it worsens during the winter. The combination of the cold harsh wind outside and central heating inside can dry out your skin, stripping it of what little moisture it usually has. Just as oily skin can be caused by over-active sebaceous glands, dry skin can be caused by under-active glands. This can be caused by hormones, environmental issues, or your skin care routine. If your skin isn't producing enough sebum, you'll need to help it out with a more intensive moisturiser. Dry skin can often be quite sensitive, so be wary of harsh cleansers and toners which may dry your skin out. It also may sound obvious, but make sure that you're keeping your whole body hydrated. I encounter dry skin more often on performers who work under hot lights all day, and who don't drink enough water. Hydrated inside = hydrated outside.