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How to make 
Mitered Lap Joints 

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V-Groove Router Bits
V-Groove Router Bits

Mitered half lap? It's not so tough! If you have a router and can read a rule, then your all set! 
I'm making a pair of L shaped pieces to form a shelf. The picture at left is half the joint. Where this is 3/4" stock, I made the depth of cut a whisker under 3/8". I Know I'm going to need to tweak this joint to make it fit right, I'd rather remove stock than shim the joint.  First, layout the 45 degree layout line on the top of the longer board. Clamping will be easier later on when we assemble the joint.
Chuck a 1/2" straight cutting bit in your router  and measured the distance from the edge of the base plate to the edge of the bit. 
Then transfer that dimension from the layout line to the straight edge that my router will use as a guide or fence. I prefer using something machined, so I know it's straight, instead of a piece of wood. This level will guarantee the mating line between the two pieces will be tight.
Start nibbling away the stock, beginning farthest from the straight edge. Be very careful to keep the router base tight to the work surface. If it tips you will gouge up the surface of the joint area. Now this is a large glue surface, and surely a couple of gouges won't matter that much. Just do your best not to damage the edges or the area closest to the fence
When you get close to the fence, be sure there are no wood chips between the router's base and the fence. You want this line perfect!
Now double check....ahhhh perfect!
After the first half is done, I take the mating piece, cut the angle, in this case 45 degrees, and lay it on top to check for square.
For some strange reason, the walls in this home are square, so I'm looking for 90 degrees here...Nice!
Now flip that mating piece over, and use that same dimension to place the straight edge again. This time at 90 degrees. The pic at left was taken after this half of the joint was cut.
When you route and area like this, you really only have one shot at getting it right. This is because at the beginning of the operation, furthest away from the straight edge, the router is supported by stock that you will soon remove. So if you don't cut deep enough, you have no way of taking off a little more. But you certainly don't want to take off too much! I went a whisker shy, I would rather plane off 1/64" then try to shim it!
Also, when you route a field this large, you will get ridges. No way around that. A small hand plane makes quick work of cleaning this up.
Ahhhhhh, looks wonderful! And it's almost perfect. A little sanding will finish it off.
Here is a view from the bottom. 
This view shows both pieces. The top piece is upside down to show the joint.
Ok, now lets glue it up! Keep the glue away from the inside of the corner, you don't want any glue squeeze out messing up that corner. Don't get too much glue on the miter either, for the same reason.  
I know, lots of people keep a wet rag around to clean up this glue. I believe this only creates more work. The glue gets thinned and runs into the pores of the wood. This will effect how stain and finish look. Save yourself some headaches and be neat with the glue!
Just a view so you can see how big this thing really is. The long leg is eight feet long. The short leg is under four feet.  
Remember earlier I mentioned making assembly easier? This is why, see how my bar clamp is placed on the short leg? If the joint was cut the other way, with the first cut on the short leg, you would need a much longer bar clamp. Either way will work, but why lug around an eight foot bar clamp?
Ok, Now I'm going to make this thin shelf look heavier, with out the expense of using thicker stock. What I did was buy 1x10 oak for a shelf that was only going to be 7-1/4" deep. I ripped the shelf to width, and kept the small strip, to place underneath like in the pic at left. Doing this ensures the wood will match in grain and color.  

So you end up with a nice smooth joint, you must drill the holes one at a time. Put in a screw, flush up the pieces for the next screw, drill that hole, then put that screw in, and continue down the length of the joint. It would be hard work to sand this joint flush after assembly, especially in the corner, so working the joint during assembly makes less work later on.

To drill the holes quickly and accurately, I like to use my tapered drill bits and my insty-drive set from Rockler. Mine is an older model and looks different but it does the same thing. The system allows you to drill a hole, then pop on the driver to put the screw in, then quickly change back to drill another hole. 
I do this step dry, without glue. It takes awhile and you don't want glue dripping on the face of this joint. Also I keep the screws well back so when I round over the top and bottom, the router bit won't hit the screws.
So after I drill all my holes and have all the screws in, I take them all out, and head to my router table with a V-groove bit installed. It only pokes out 1/16th of an inch or so. 
I set my fence so there is about 1/16th of an inch between the groove and the face side of the joint. During assembly I will keep the glue behind this line, and when the screws are tightened, any extra glue that would squeeze out onto the face, will be caught in this "glue gutter".
The top pic here shows glue squeeze out on the inside of the joint where it won't be seen, but the lower pic showing the face is spotless!
With a little stain and finish, it don't look half bad!
Here's the left side. 
Takes up lots of space in the shop!

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