Sketch of Foley catheter with labels. Sketch from USPTO (public domain), text labels added by cpony.
This article is on urinary catheterization whereby the pony's vet will insert a tube up the pony's urethra until it reaches the (urinary) bladder. Catheter play can be really fun if done safely and in a sterile manner, but you do need to be aware than even if performed properly, there are risks of infection and damage to the lining of the urethra. This type of urethral play is veterinary/medically oriented play and differs from the electrified urethral rods/inserts used in some types of ponyplay training.
Note: be careful if you choose to engage in catheterization play. I would strongly discourage using a catheter to prevent emptying of a pony's bladder. I would even more strongly discourage using a catheter to force fill a pony's bladder.
Catheterization in ponyplay is most often used as a form of bladder control. Once inserted and fixed in place, the catheter can be used to force continued emptying of the pony's bladder, or, alternatively, to prevent emptying of the pony's bladder. In fact, a urinary catheter can actually force more fluid (usually sterile saline) into a pony's bladder. This will "force fill" a pony's bladder. This can cause immense pain since the bladder can be completely filled with fluid and then closed off to prevent any emptying since the catheter is the only way the fluid can get out.
Thus the pony has absolutely no control over bladder functions, which is of course humiliating. If the vet leaves the catheter open the pony cannot prevent emptying of the bladder and urine will flow out as soon as it enters the bladder. Conversely, if the vet closes the catheter, the pony has no way to empty his bladder regardless of how much he needs or wants to. So aside from the humiliation aspect of catheter play, there is also potential for pain and other sensation play.
Placing a catheter requires sterile technique to avoid urinary tract infections (even when placed with proper sterile technique, urinary catheters will still gather bacteria in a day or two). Moreover, tissue damage can easily result if improper technique is not used in catheter placement. If you do decide to engage in catheter play or other forms of vet play, please do be careful and make sure both you and your pony are aware of all the risks involved.
I will discuss the placement of a Foley catheter here since it is one of the most common types of urinary catheters, and the only one with which I have direct experience. Below is a diagram of a Foley catheter. The Foley catheter can be used on either male or female ponies. I will start by describing the procedure for catheter play with either a ponyboy or ponygirl. However, be aware that catheter play with ponygirls can be more prone to infection.
Sketch of Foley catheter with labels. Sketch from USPTO (public domain), text labels added by cpony.
So let's begin. You'll need a few items to catheterize your ponyboy or ponygirl (you can buy all these items together in sterile "catheter kits"):
With your ponyboy (or ponygirl) safely restrained begin by preparing a sterile field. Use the surgical scrub to clean the area (penis and surrounding area if it's a ponyboy) and put on your sterile gloves. Fill the syringe with sterile saline and connect it to the appropriate filling port on the catheter (balloon port on the diagram above). Check the balloon on the catheter for leaks by slowly depressing the plunger on the syringe - the balloon at the end of the catheter should fill up and remain filled.
Deflate the balloon by removing the saline with the syringe using the balloon port. Apply the sterile lube to the end of the cathter. Separate the labia (or hold the penis in a perpendicular position) with one hand and clean the area once more with the surgical scrub. Now, still holding the penis in a perpendicular position (or if a ponygirl, still holding the labia) insert the cathter up the urethra. Continue inserting the cathter another inch or two after you first encounter urine. Inflate the balloon with sterile saline using your syringe - check the information on the catheter packaging to confirm the correct amount of saline needed for proper inflation - do not over inflate.
Once inflated, pull the catheter down slightly until it is snug with the bladder wall (do not pull too hard). Following correct placement, connect the tubing to the urine drainage port of the cathter and connect the tubing to the collection bag.
As noted above you can force fill a pony's bladder by using a syringe (filled with sterile saline) to push fluid up through the urine drainage port. The port can then be clamped closed to keep the bladder full - depending on the amount of fluid pushed in, this can certainly create sensations range from interesting to uncomfortable to painful. Obviously this is not recommended and can be quite dangerous.
Catheter play can be incrediably fun. There is a sense of being completely controlled with catheter play that I can't really explain. To have my bladder forcibly filled or emptied at the whim of my vet/trainer really imparts a feeling of helplessness like nothing else. Be safe and have fun!