Patios, by nature, seem like a bit of a tease. They take up space in the yard and keep the ants off of your toes, but they're not actually useable rooms in the normal sense. This is especially true in the United States, where home builders sometimes lay down a concrete slab or extension from the home and call it a patio. Enclosure options vary, as do the laws regarding them.
Walling a Frame
If your patio or veranda already has a roof and a full perimeter frame, then it's already a room without walls and insulation. The simplest solution is to just put up the necessary vertical studs with the correct center-to-center distance and then build walls and windows like you would any other room. You're probably going to want to insulate the roof and floor (if it's a suspended deck-type patio) and install a ceiling. Other than that, a perimeter-frame patio is just a room waiting for walls.
Building a Florida Room
One option you might consider is framing in between your main support columns to create regular space intervals, then filling those intervals with glass instead of wood. Florida rooms are a cool addition to any home, and you can keep yours even cooler by using double-paned windows with a polarized one-way tint on them. The polarized tint will keep both the sun and prying eyes from poking into your sanctuary. Consider installing low-wattage fluorescent lights on your vertical supports; these lights will work like the pillar lights on a limo, making it nearly impossible for anyone to see inside.
With or without a roof, concrete patios are generally an integral part of the home's foundation. That means that, according to the zoning commission, the patio is already a part of your house. However, you'll probably still need to get a variance or waiver to fully enclose the patio and incorporate it into the home. The line can be hazy in some areas, but generally speaking, but if it's attached to the house, air-conditioned and shares electricity with the main structure, then it's a part of it. This is especially true if you have to build a roof and framing, since that definitely constitutes an addition and will need to meet zoning and building code regulations. Again, specific laws vary by state and jurisdiction, so check with city hall or ask a local contractor to point you in the right direction. Screen isn't considered a wall or window, so screening a patio usually doesn't require a permit.
Most jurisdictions don't require a variance for portable or free-standing structures that aren't attached to a foundation; such structures will generally fall under the same auspices as car ports and titled trailers parked on the property. The key word here is "portable," which Websters defines as "Able to be easily carried or moved." So long as the structure is free-standing -- not attached to the home or foundation using any sort of fastener, glue or sealant -- and the walls and ceiling are joined using through-bolts and nuts, then you could certainly make the argument that the whole thing is free-standing, capable of being disassembled and ultimately "portable." But all of this is fairly academic anyway, since odds are good that if you already have an existing concrete foundation or deck then it's already been zoned and you'll be granted the appropriate variance to wall it up.