Well the most important thing is to actually think about everything you're about to do when connecting a circuit.
Check if the oscilloscope probe's ground pin is shorted to the power supply's ground pin (in most cases it will be). Check if output pins of the power supplies are connected to ground pin. They might be, but good quality supplies will have separate ground pin available on front. Also check if the PSU case if connected to ground (it probably will be) and if it is, take care not to have a positive wire touch it.
Every time you connect the scope to something powered by the power supply, think what's going to happen. I've seen cases where people shorted-out their power supplies using oscilloscope probe ground pin and couldn't realize why that happened.
Next, check how the power supplies are going to react in overcurrent situation. Is it going to shut down or will it drop voltage or something else? In general, familiarize yourself with equipment you'll be using.
Do keep in mind that a multimeter in current measurement mode is basically a short-circuit and in voltage mode is basically open circuit. Take care how you connect it! Do read the manual and try to understand what happens in other modes, if there are any. Take note of maximum voltage the multimeter can take with each of them.
For the end, once again, read the equipment manuals and try to plan out each situation in which you can find yourself in as far as the equipment is concerned and think about what will happen if you make a short somewhere.
ABOUT THE COMMENT:
The problem has to do with "floating" and "ground-referenced" power supplies. When a power supply is said to be floating, it means that you can't make a current loop which goes back to ground. An example of this is a battery-operated device. Current goes from one terminal of the battery to another and if you connect one side of the battery to the ground, no current will pass through the wire, because there isn't a closed loop for current to go through. Take a look at this simulation where the ground is connected to the positive output of the battery and no current goes through it.
Same thing happens when you have a transformer separating the mains side of a power supply from the low voltage side of the power supply. All current going out of the secondary side of the transformer needs to go back into the secondary side of the transformer and if you touch a wire along the path, no current should go through you since there isn't a loop for it to go through. Take a look at this simulation. Here too we have ground on the secondary side of the power supply and co current goes through it.
Now to get back to measurement instruments. A hand-held multimeter is often battery powered and is therefore isolated from the circuit it is measuring. This allows you to for example connect the negative probe of the multimeter to the positive pin of the power supply and positive probe of the multimeter to the negative pin of the power supply and the measurement will work, but you'll get negative voltage.
On the other hand, most oscilloscopes are connected to mains power and the ground pin of the probe will usually be connected to the ground pin of the oscilloscope's power supply. On some bench-top power supplies, the negative side of the secondary is connected (or can be connected) to ground. If you for some reason connect the ground pin of the scope probe to the positive pin of the power supply, you can create a short. It will look something like this.
That supply could very easily kill you.
That said, I've (long ago) had a number of shocks at that level with no long term ill effects - BUT some people manage to die on the first encounter. Try not to ever find out which category you will be in. (I've also had numerous 230 VAC mains shocks and a few at around 1000 VDC with in all cases never more than a nasty experience at the time.The last was long ago and I aim not to repeat them if at all possible.) (230 VAC is probably the most "disturbing")
A DC supply has a "can't let go" effect clamping the muscles. You don't want to EVER experience this.
HV is not something to worry about overly much - but must not be ignored. You may be able to receive say 100 shocks in quick succession from such a system and suffer no consequesnces apart from nightmares and a lifelong aversion to digital clocks of any sort. BUT it could kill you along the way.
Anything in the area outlines in red in the diagram below will be potentially lethal and anything outside it MAY be :-).
Historical advice is to keep one hand in your pocket while testing to prevent accidentally closing a hand to hand circuit via you chest/heart. That has some merit BUT slow deliberate thought out actions are at least as valuable.
Rubber dish washing gloves would offer very substantial protection if dry and not punctured. Puncturing can happen on a small wire end. They can be used as an added safety feature and PROBABLY make things much safer BUT act as if you are not wearing them.
If I "MUST" work near live conductors I try to keep fingers curled inwards so that a hand clench triggered by current will not cause grasping of a live conductor. Brushing the back of a hand against a live HV conductor is liable to cause a muscle contraction towards your body BUT do not ever rely on this.
Best method is to have HV turned off until it is needed for testing.
Think what you are going to do, and have tools, meters etc ready.
If you can attach a meter with a test clip with power off, so much the better.
If a test clip will not safely and reliably attach to the HV target you can solder a wire to HV when power is off (of course) and connect that to the meter probe. After you have experience with such things you are liable to think nothing of measuring say 230 VAC mains or 500 VDC with two probes with power on - but resist the urge to leap in an do what will be safe enough wit experience until you have some experience - or you may never acquire any :-(. It's really rather safe most of the time. But it's better to be safe than sorry as a beginner.
Power on, think, test, think, power off.
Be SURE power is off.
Be SURE power is off.
Be SURE power is off.
I have seen power on when it was thought to be off happen often enough over the years that I am quite obsessive about checking. If a mains cord is involved I am liable to turn power off, pull out plug, wave the cord to be sure the plug is the correct one, place plug near gear being worked on as an indication that it is safe. That's obsessive. I'm alive.
I recently installed a new domestic stove in place of an old one for a friend, with only a wall mains switch between me and mains. Fuse still in for various reasons. "Safe enough" but potentially lethal. Tested with meter. Shorted all leads (PNE) together to ensure no mains on.
Treated all wiring as if alive as much as possible throughout job. Obsessive. Alive.
Think carefully. Act slowly. Being very safe is easy.
Best Answer
If the plan is to sell the product your designing, then odds are you'll want to certify your product with an ETL. Most products fall under IPC-61010, and exception would be if it's IT Equipment, Medical Equipment, ect. Use the specs for the product group that the to be designed product falls under. All of these specs are pay-walled, and are not cheap. I'll summarize parts of 61010 to give an idea of what is required, but it would be best to find a regulatory consultant.
Source: Electrical safety and isolation in high voltage discrete component applications and design hints
The two main ones that I can think of are shorting and a user coming in contact with the wire.
If I remember right (not completely sure) voltages are not considered hazardous until after 60VAC or 75VDC. I've ran 48V on a PCB and through a cable to a heater and didn't have to take any special precautions for user safety but that portion of the product was in a user inaccessible enclosure.
Whatever voltage you have in the design, it will need to conform to certain spacing. PCB's and wire assemblies have different spacing as shown in the chart below. Pollution degree of the product (dirt makes arcing more likely) determines how far the wires or traces must be placed.
Source: http://www.pcbtechguide.com/2009/02/creepage-vs-clearance.html
The user of the product needs to be protected against electric shock (see section 6.1.1 of 61010), during normal operation or a fault. If the hazardous voltage is not accessible to the user and requires a tool, then a warning sticker can be placed on the product to make it sufficiently safe.
As far as the tubing, I'm not aware of any requirements for the material for insulation. The main thing 61010 is concerned with is materials for voltages over 100V which are prone to arcing. That being said it would probably be a good idea to get a tubing that has some kind of IEC certification. I would think that it would need to be flame resistant.