I make frames a lot for my artist wife. I prefer miter joints, but you could make what you want by cutting a rabbit on the underside of both the long and short pieces. Then cut the same off the top edge of the short pieces. Fit the two together with glue and short brads up through the back side to hold them in place while the glue sets. Glue will hold very well.
You can use a bit like this to cut the rabbet. They are available in many sizes. The width of the rabbet is a function of the placement of the bearing. The bearing size will determine the width of the rabbet. This shows the set and profile
If you are using a lap joint, the depth of the rabbet must be half the thickness of the material. If you are using 3/4 inch thick material, the rabbet must be no more than 3/8ths deep. If it's not exactly half, the face of the frame will not be even at the joints. In a way, you are making a face frame, but a picture frame doesn't need to be as strong.
It does need to be square, however. so cutting the ends, particularly of the short pieces, must be exactly 90 degrees. If it's not, you won't be able to make the frame square. At best, you'll have gaps at the joint lines. If you don't have a table saw and a very accurate miter gauge to make exact 90 degree cuts, then I recommend you buy a really good miter box and use a japanese "pull" saw to make the cut. There are also American made pull type saws, they cut on the back stroke so the cut is cleaner. Both have fine teeth. It's 90 or a mess. Here's one from Amazon for $23.
https://www.amazon.com/Deluxe-Razor...082106&sprefix=pine+litter+box,aps,242&sr=8-8
With frames, you have to make sure the opening of the rabbet is just about 1/8th inch larger than the canvas.
There is a formula for computing the size of the frame opening, but in essence it is the width of the cross pieces, plus twice the width of the stock. That more or less give you the inside dimension of the opening of the frame. You generally want to have the rabbet opening just slightly larger than the size of the canvas or the flat art, or the size of the matte board you're using. Takes a little planning.
Finally, once you get that 90, then you have to run the short pieces endwise to cut the top rabbet on the ends exactly the depth of the width of the rabbet. EXACTLY, or you get to sand and sand and sand and sand to even it up. The easiest way to do this is to use a square of MDF or plywood to back up the workpiece. This is pushed flush against the fence and you hold the piece firmly against the block.
I like to make frames from hardwood because I don't like the rustic look all that much and want frames that are suited to the painting. I buy stock from a supplier 50 miles away, and the end is nearly always unusable due to warp or splits. So I have to buy extra. Cost for milled frame stock in my favorite (cherry) cost about $40, probably more after the Biden price hike. And there is a slew of expensive, specialized equipment for making perfect frames. Pay $150 to $300 for a frame and you expect perfect. I have thought lately of buying some of the cheap, oversized frames from Asia and cutting them down to make frames to fit my wife's smaller works. But I must then deal with whatever finish they happened to use on them.
There's a great little book, called the Joint Book, available on Amazon. It covers all kinds of joinery techniques, and a little help on how to make them, on heavy, laminated card stock so you can keep and use it in your shop. I use it whenever I want to do a special project. Get the spiral bound version, it lays flat.
https://www.amazon.com/Joint-Book-C...=1646084786&sprefix=The+Joint+,aps,179&sr=8-1
