As a start, choose neutral off white mats either warm or cool depending of the overall hue and value of your painting. After you've been at it a while and have seen what others are doing with colors and bevels and layers feel free to experiment. But fancier mats are best left to your local framers or purchased precut.
With precut frame and mat sets you will paint your painting to fit a particular frame and mat size, so test your painting during it's dry stages by laying the mat on top and work with that shape in mind. A lot of artists commit to working in only a few standard sizes where the whole process from easel to installation is simplified. Smart or lazy? Six of one...
Otherwise you cut your own mats and order quantities of your own pre built frames or buy frame kits at your local art store. This method also works well for preparing a large quantity of matted pieces for an upcoming show or (gasp!) art festival.
Materials: 2 pieces mat board, heavy metal straight edge, a sharp pencil, and xacto knife with fresh #11 blades or a mat/utility knife with new blades. A roll of linen tape. The tape usually comes in a boxed roll, the actual tape must be peeled from it's backing before securing. And you'll need a large flat surface you can cut things on with abandon.
Always be aware of where your fingers are in relation to the sharp blades you'll be using. (Duh)
You have two layers, a front and a back, or top and bottom, whatever fits your perceptual orientation in space. Both pieces should be larger than your painting and cut to the size of the frame you will ultimately use. The top piece is the decorative mat side with a finish and color that should compliment the piece you are matting. The bottom is usually a heavy gauge museum rag board in neutral gray. After determining the actual dimensions of the image you want to reveal through the mat, subtract the image dimensions from the mats outside edge dimensions. Split the difference and you have the dimensions to measure in from each edge to mark your top mat.
Think about it.
Once you mark your top mat lightly with a sharp pencil and lay your art over top just to see if it's looking right, take an xacto knife and in each corner of the hole you're going to be cutting press the tip of your #11 in the very corner and make a slight but thorough cut on each point of the corner, the motion is sort of like slicing a sandwich. You just want a clean corner cut that allows you to cut the long cuts easier. You really don't want to make an over cut while cutting a corner, that can ruin your day. Rotate your mat and do the other three corners.
Next take a METAL straight edged ruler, the heavier the gauge the better, and lay it to the left of the left line with the mat lying flat in front of you. Align the straight edge and press it firmly with spread fingers of your left hand. (NOTE: You are NOT trying to cut all the way through on the first cut.) Take your xacto or mat knife (with fresh blades) and starting at the corner cut, pull a cut with a firm but controllable pressure, letting the blade align and slide down the ruler as you guide the cut through to the other corner. Too much pressure on the blade can cause you to slide or fumble due to imperfect grain in the board. Make direct, confident, and smooth cuts. It can take 3 or more good cuts to get all the way through. You can notice the sound of the cut change as your blade exits the other side of the mat board. Sometimes once I make the initial cut, I move the ruler off to the side and do the final cuts freehand. It's a good challenge.
After you complete all four cuts gently lift the edge nearest you and gently push the cut out to make sure you cut it thoroughly. If there's any stuck bits use your knife to cut them cleanly. You now have a Window.
Lay your bottom mat down, lay your top mat on top of it sandwich style. With the top edge of the mat sandwich to your left, lift the top mat like a page in a book, up and left and over, and lay it next to the bottom mat. Align the edges that are butting together. Take a precut length of linen tape and lay it straight down the middle of the abutting pieces. Press it smooth. Reinforce the outside hinge corners with strips of 4-6" tape (see illustration) Fold the page back over to the right, like you forgot what you read on the previous page.
Lift the top mat and slide your art work into the mat sandwich. Lower the mat, take a look, lift the mat, move the art a bit, lower the mat, take a look. Once it's aligned in the window to your liking, gently lift the top mat back and out of the way. Pressing lightly on your artwork mark the corners in pencil on the bottom mat board surface. The painting should be hinged at it's top edge using rice paper hinges (see illustration) instead of linen tape. If for some reason the painting is torn from the mat board, the rice paper will tear leaving the painting unharmed. (I have often used linen tape for this purpose with no obvious problems to date.)
If you are preparing a large batch of matted pieces for sale at a show or such you would stop at this point and back your pieces with 1/4" foam board and shrink-wrap them. It is an ideal temporary storage/display strategy for selling loose artwork. And it looks more like professional product.
You have a matted painting whose exact dimensions match your frame. You assemble or unpack your frame. With the frame laying face down and stripped down to the glazing (Plexiglas is recommended) take time to make sure it is clean and free of all dust and debris. Check your matted piece to make sure it is clean and slide it face down against the glazing. There is usually a backing piece of cardboard that nestles on top of the back of the mat. If not, cut your own to size from a piece of foam board 3/16" to 1/4" thick.
While things are still loose, hold it all together and flip it over to make sure no debris or stray cat or dog hairs have snuck in between the glazing and the top mat. Secure the backing board by what ever method your frame has available. Some have pre-bent tabs, some have tension clips, wooden frames require brads or if you frame a lot invest in a Framing Tool that drives framing points (small, flat metal shapes) with the click of the lever. You may finish the back by using brown tape to seal over the edges between the mat and frame. It helps keeps dust and moisture out.
Next set your screw eyes. They come in various sizes depending on the weight of the piece you'll be hanging. On wooden frames I generally measure 1/3 the distance down from the back top edge on each side. If it is soft wood you can start driving the screw eyes with your fingers until they catch. They can be further tightened by inserting a small screwdriver in the eye to use as a handle to twist. If you're using hardwood you must tap or drill a pilot hole first. I've had many screw eyes snap off during tightening in hardwood. Metal frames usually come with their own special loop fittings that slide along an internal track and lock in place. You can also install "D" rings on a heavier wooden frame which lie flat in a thin metal bracket allowing the frame to hang closer to the wall.
Measure a length of hanging wire (a braided soft metal wire) about 6" longer than the gap between the two screw eyes. Loop one end through the eye about 3" and bend it back and twist the cut end around the wire, securing it to the eye. Loop the other end and snug it through before you twist and secure the wire. Over time the wire will stretch a bit so you don't want it too loose.
When hanging your art take the time to use actual picture hanging hooks. They are designed so the nail secures strongly at an angle and the hook allows the picture wire to hang and slide freely without binding. If your walls tend to chip, lay a piece of tape over the mark before you drive in the hook. Any dust or chipping from the nail will be secured by the tape. You could also end up with a 3" crater in your wall...depends on the age and structural integrity of the walls. It happens.