There are four major aspects to the proper fit of a western boot. These are:
Each boot has an area in the front called a 'toe box'. Underneath the leather within this toe box is a resin soaked, fiberglass like piece of cloth which has been hardened so the boot will keep its shape. This area will never stretch! Therefore, it's important that you are able to wiggle your toes. They shouldn't be pressured by the front of the toe box, the top of the toe box, or the sides of the toe boot.
The boot should hold the ball and instep of your foot much like a firm handshake. Since this is the only part of the boot which holds it onto your foot, it's quite important that this area be snug. The boot should not be so tight that there is pain or discomfort, but this part of the boot will stretch with use (except for some exotic skins), so a snug fit here is important.
As you walk in new boots, the heel of your foot MUST rise up away from the sole of the boot just a little bit. We describe it as a finger's width of rise. If your heel is rising up more than an inch the boot is either too long or too wide. Some rise is normal, and will diminish as the boots break in. This happens because the sole of the boot is very stiff, and doesn't flex quickly. As you wear them and the boot molds to your foot, this slippage won't be as noticeable.
There is a break in the boot between the heel and the ball of the boot. This break must line up with the arch of your foot. If it does not line up, you may feel a line of pressure across the bottom of your foot -- almost as if you were standing on a ledge. Or it might feel as if something is pushing up on one side of your foot. It's important to note that, if you've been wearing sandals, loafers, or tennis shoes, the support offered by cowboy boots will feel quite different from your shoes. Only you can tell if the pressure you feel is because of the support, or because something doesn't line up. If an arch doesn't line up, then generally speaking you should try a different brand of boots. Every manufacturer uses unique molds for their boots. If you keep searching until you find the size/brand combination that fits you best, you'll be a happy boot-wearer for life.
Your foot should not slip into a new boot easily. A properly fitted pair of boots will require some effort to pull on. Ideally, there is a hesitation, and then a THUD as your foot falls into the boot. Also, your feet are not 100% symmetrical. One is larger than the other, or longer, or wider, or has a different instep height. Regardless, one foot will slip a bit more in the heel than the other. This is natural. You are better served by fitting the larger foot, as extra room in one could be taken up by an orthotic, or an extra sock, or a thicker sock. However, if a boot is too tight there is very little that can be done. Actually, if it's too tight in the toe box, then nothing can be done except to exchange them for a longer size.