There are many different joinery techniques. Although most recommend some type of screw or nail for additional strength there are some that will work without them.
Two of the most common would be Mortise & Tenon joints and Dovetail joints. There are many different variations of these types of joinery.
If you do not want to use unsightly screws, nails or staples you may still want to consider using dowels for added strength.
One good source of information for various types of joinery would be Wood joints, [Joining wood, Dove tails, rebates, mitres
There are many other sources also available.
Know someone who might be interested in this post? Please like and share this post with them. If you have questions or comments please leave them below.