Once the glue is set and the work is rigid, the other three pieces are lined up and attached with glue and screws or brads as before. Like much woodwork, it is a process of construct and wait for the adhesive to cure. In some ways it is bit like planting a seed and seeing what happens.
When the glue is cured, about eight hours later, the stand is set on its base and is essentially done. Do not make this compicated.
I have used good construction lumber as well as good but used scrap wood to make the stand. As can easily happen in such a case, a bit of inspection notes a weak spot on the left rear 2x2.
A closer look reveals a spot where an injury happened to the tree in its past life. It looks like a branch got torn off and some rot set in. The spot is solid around it but there is some wood missing, leaving a hole part way through. It is probably plenty strong for our purposes, after all a 250 pound man sits on a chair with legs no more than an inch around, but a little insurance can not hurt.
So I cut a piece of scrap to fit and glue and brad it into place. All the brads do is hold things until the glue sets. clamps would be fine. Today's glues will hold with a strength that exceeds that of the woods they are used on. In other words the wood will give before the glue does.
The spot in the room for the plants has been cleared and the stand will go where I have a strip in place on the wall. This is not necessary but a bit of added insurance. The strip has an angle cut in its top edge which will fit an angle cut into the edge of the top rear strip on the stand. It is an old way of hanging cabinets and will give a bit more support to the stand.