Do not look down on it. The fact that some in magic avoid the Square Circle because they think “anyone can do it” should be ignored. Those who think that, to prove you are a good magician everything you do must involve a sleight or a move, are wrong. An important aspect of magic is knowledge and secrets. The fact that the secret to the Square Circle trick is simple (a black tube hidden inside a square box), does not change the reality that, when handled properly, it is an amazing trick.
Do not take the secret for granted. It is true that the trick works because of the black art principle, but it is also true that the trick can be done well or poorly. It is not enough to have a black tube in an open front box. The way the prop is handled and displayed is important. Important enough to think about carefully and then practice.
With most versions, it is possible to make the audience think they have seen the inside of all parts of the prop. Do this by beginning with the load in place, inside the circle, which is inside the square. Lift out the circle, leaving the load in the square. Show the circle empty. Put the circle back into the square. Lift up the square, leaving the circle behind. Show the square empty. Then, before putting the square down, pick up the circle and, by way of finger pressure inside the load tube, pick up the load tube as well. This allows you to lift up the circle and load tube, which shows nothing on the table. (Square is in one hand, circle and load in the other.) Next, put the square down. Finally, put the tube and load down inside the square. Experiment with this. You will find it to be effective and convincing.
Do not do it on a “box table” or draped table. This should be obvious, but many fail to understand the importance. If the Square Circle prop is positioned on a box type table, or a table covered with a drape, audience members will think the items produced are actually coming from within the table. The best way to use a Square Circle prop is with it on an elevated base that people can see beneath, or else on a side table that is simply a support pole and flat top.
If you must use the Square Circle on a box type or draped table, after showing it empty, turn the square on its side so the audience can see through it, and put the circle on the square. This means you will make the production out of the circle, while it is separate from the square. The advantage is, because it is on top of the square, the audience will know the production is not coming out of the table.
The production should seem to be larger than what can be contained in the prop. It is not impressive to produce a small stuffed Teddy Bear from a big box. People think, It must have been hidden in there somewhere. What you want them to think is, There is no way that could have been in there! This is why big silks and long streamers are especially good as production items. When displayed, they seem bigger than the prop itself.
Figure out how to load the prop with a production that seems impossible. An example would be to have a large ball in the load tube. The ball is hollow and has a hole in the back (that the audience will not see) so production items fit inside. The smaller items are produced first, then out comes the big ball. Instead of a ball, it could be a globe of the world. There are many ways to nest items, or put one thing inside another, to make the volume of the production seem incredible. Basically, the bigger the production is, in comparison to the size of the prop, the greater the impact of the trick.
Consider putting a shelf in the load tube. This allows production items to be above the shelf and thereby produced from the top of the tube, but also means, at the end of the trick, you can lift the square, circle, and load tube up and away to leave a load behind on the table. (If you have a large Square Circle, this final revelation could be a rabbit). The downside of this design is you cannot do the handling described under point #3 of this article. The upside is, making the final part of the production in this way is extra impressive.
Reveal production items at a fast pace. The danger of having a tremendous amount of items hidden in the prop is the audience will become bored by the extended nature of their revelation. Stories are told of magicians in days gone by who would take twenty minutes to do the Square Circle trick. Twenty minutes may be an exaggeration, but to the audience it likely seemed like twenty minutes. The goal is to have a lot in the prop and then to produce it in an upbeat and exciting manner.
If the Square Circle you own is of the old-fashioned Chinese design, consider changing the look or else come up with patter that justifies the design. There was a time when magicians would say, “While traveling in China I found this ancient box…” that is why the prop was decorated with an oriental motif. Nowadays, that line of patter seems pompous and silly. Unless you can come up with a story that gives reason for the look of the prop, it is good to repaint or redecorate it. Usually, it is not hard to give a new look to an old prop.
What to produce from a Square Circle? Many consider it ideal for use with livestock such as a bunny or doves. Silk streamers, large picture silks, spring flowers, candy, popcorn, foam items, fake fruit, small books, and stuffed toys are all possibilities. Why not find a toy elephant and then “produce an elephant” in your show!
Use real black velvet to cover the load tube. To save money, many manufacturers use black felt or velveteen. Nothing works as well as real black velvet. It is much more expensive, but worth the cost. If your load is covered with something other than black velvet, seriously consider recovering it. You will be glad you did.
Here are some design ideas for the Square Circle prop.
The “castle” look version is one I used when I first started in magic and it has served me well for many years. 
It is big enough to produce a rabbit and much more. The castle gates allow the audience to see inside the box, yet, when the circle tube is removed, the black art effect is still strong. Another advantage of the “Castle” look is it fits with stories about magical times and places.
This version is a modern looking box with a circle tube inside that is actually a phantom tube. 
By way of the phantom tube, a production can be made from just the “circle tube” as well as from the main load tube. I especially like this model of the trick, but in recent years it has been hard to find it available in good quality. I purchased a junky version and rebuilt the outer box. It was also necessary to recover the load tube.
The picture is of a “workhorse” version of the prop. 
The look is simple and practical for almost any kind of show. The design is deceptive. The load capacity is impressive. You can find this at LaflinMagicStore.com. It many not look as fancy as some, but I think the magical aspect of it is very strong. Highly recommended!