Splines are narrow pieces of added material set into grooves in adjoining wood pieces during glue-up. They function more to align workpieces than to strengthen a joint, and they are often cut from thin plywood or hardboard, so that grain matching and wood movement considerations are not a problem. If you do decide to use solid wood splines in joinery, be certain they are cut with the grain running parallel to the workpieces being joined. It would also help to make them from a wood species that is the same as or similar to the species of the workpiece, to avoid different ranges in movement during seasonal humidity changes.
There are many different ways to use splines: edge to edge joints, for instance; or when one edge of a board is joined to the face of another. They can also be added inside the full length of a miter joint, to align and strengthen it. Splines assist in leveling the planks under the breadboard ends of a tabletop, in lining up compound angles and in strengthening mitered frames.

In edge to edge gluing, splines can either be inserted the full length of the joint with the ends of the boards showing their presence, or they can be hidden inside stop-cut grooves, the splines being cut to fit and ending a few inches shorter than the boards' length. To stop-cut the grooves on a table saw or router table, first set the saw blade or bit slightly higher than half the width of the spline (on a router table, use multiple passes to achieve this depth), allowing adequate room inside the joint. The last thing you'll want is to discover your joint won't close after all the glue has been applied.

Next, mark your fence on both sides of the cutter with tape or a pencil, showing where you will lower the front end of the board down onto it and run it along the fence to cut the groove, then lift the back end of the board before the cut runs all the way through on the board's edge. This procedure leaves a rounded end in the groove when cut on the table saw, so the ends of the spline need to be shaped in a corresponding arc to fit it.
Remember also to know where all ten fingers are when handling a workpiece this way. Use push sticks and featherboards if your pieces are small or narrow enough that the cut cannot be made safely. A general rule is not to work wood shorter than 12" long or less than 1/4" thick on woodworking machinery without a sled or added jig to stabilize it.

Another use of splines is as reinforcement in corner miters, as in the flat faces of a picture frame. Squared-up frames with mitered corners can utilize quite wide pieces, so the miter joints are weak and cannot stand up to much stress. In this case, a spline is a helpful support to the joinery. To cut the spline's groove in a corner joint, a sled or fence accessory is usually made in the form of a 90º V: a "cradle" to rest the mitered corner in as it is passed over a table saw blade or a router bit in the table. The deeply cut groove is then filled with a spline, then the excess is trimmed flush with the level of the frame. These splines can either be done in contrasting wood for a decorative effect, or in similar wood to be camouflaged by the frame. The grooves can also be cut with a handsaw, but practice on scrap wood first. Handsawing absolutely straight lines, to a particular depth, is a skill needing a little practice.

Splines are also good for aligning compound angles for glue-ups. Say you are assembling a lamp base of six tall pieces angle-cut to form a tapered hexagon 21" tall. At the inside, narrow edge of each bevel, a shallow groove can be cut to receive the spline. Once again, be sure the sum of both grooves' depth is slightly more than the width of the cut spline, to allow adequate clearance for the joint to close tightly.

Splines can be a useful, hidden aid in complicated joinery, or have a decorative effect when highlighted with a contrasting wood and left exposed in the end grain of a workpiece. Experiment. Your goal is a slip-together fit with adequate depth clearance for glue, requiring only hand pressure to assemble with no side-to-side play or looseness in the joint. Spline joinery is a useful technique to add to your woodworking repertoire.