Either sewn or crocheted, each seaming technique posesses its own special qualities. Corresponding yarn and a blunt darning needle are used for the sewing methods; a crochet hook is used for the others.
1) Single Crochet. This is a decorative seam on items with two pieces (front and back), like a pillow or tote bag, etc. It is sometimes used to stitch together afghans motifs where the ridge-like stitching is intended show.
To work a single crochet seam on a pillow or tote, place the wrong sides (what becomes the inside) together and use single crochet all around the edges. Simple as that.
When working single crochet to put stich afghan squares or strips together, butt the pieces together with right sides (fronts) facing. Stitch away.
2) Slip stitch. Less decorative than single crochet edging, this is also intended to show on the finished project. Again, it is useful for items with a distinct front/back and afghan motifs and works exceptionally well when attaching a pocket or pouch. To join items, work much the same as single crochet (above). Use the same yarn and you get texture; use contrasting yarn and you get texture and a pop of color. For adding a pocket, after placing it in the spot desired, slip stitch around it and through the 2 pieces to be joined.
3) Mattress stitch. Leaving only a small ridge on the wrong side of the work, this method is almost invisible and best used in garment seaming. Since it is worked with the front (right) sides of the work facing you, seams butted together, you can actually see how the seaming progresses. To work mattress stitch, place the project pieces, edges together, front sides facing you. Thus, there is a right piece and a left piece, fronts facing, edge to edge. With a darning needle and corresponding yarn, secure the yarn at the edge where you begin. With the needle pointing up, pick up the first stitch, leaving yarn loose; go to the opposite piece and pick up the corresponding row. Continue in this fashion and after three to four stitches, tighten the yarn so it "disappears, but not so tight that it causes your seam to pucker. Basically, you're creating a stitched zig-zag and cinching it tight after a few stitches.
4) Backstitch. Sturdy and popular for seaming together garments, this stitch leaves a bulkier seam than mattress stitch, but is very strong for sleeves, shoulders and underarms. With right sides together, with darning needle and correspondening yarn, secure yarn at the edge of one piece before piercing both pieces. Push the needle through both pieces at once, working across from right to left. Come up through both pieces at point A, make a stitch backwards and come up at point beyond where you made the first stitch. Imagine each stitch as a half inch segment in which the needle first pierces both pieces from back to front at point A, then pierces the pieces from front to back a quarter inch distance to the right, then pierces the pieces again from back to front half inch, repeatedly. Pull the stitches tightly to hide them, but not so tight that the seam puckers.
5) Whip stitch. With darning needle and corresponding yarn, hold two pieces together and insert the needle from back to front, continuing around and around (think of the stripes on a candy cane). This method is simple, and very good for seaming together afghan motifs. Worked on motifs through the back loops only with "wrong" sides facing, the stitching is almost invisible when the same color yarn is used, making the front of the project look as if the front loops of the stitches have become one. This is a basic, sturdy stitch. It can also be used for garment seaming where a "rustic" look is desired, but is rarely recommended for garments. I personally like this method for seaming garments..call me crazy.
If you would like to practice seaming, make a few squares of the same size. Seam them together using the various methods. It is a practice piece; it doesn't have to "be" anything.
As always, look to the internet for photo or video tutorials.