How to touch 'em, how to not touch 'em, and what to do if you've touched 'em—all by a person who currently has several spines embedded in them.

Spines versus glochids

First a word of caution: large spines look nasty, but in reality you will find yourself cursing glochids far more often. Big spines are a warning: your brain knows to respect those giant scary spines. You get poked, you'll make an effort not to repeat it.

Glochids are the tiny tufts of spines some cacti have in the place of spines, or around the base of their larger spines. If you don't see any spines on a cactus, operate under the assumption it has glochids. They easily stick in skin, clothing, plastic bags, styrofoam, anything soft really (including the hose, I have learned). You won't think you even got near a cactus and somehow you'll have a patch of forty teeny spines that zap you when brushed.

Glochids can be near-invisible and spread extremely easily; I have watched glochids waft off of a cactus because I nudged its pot. If your shirt brushes against a cactus with glochids you will quickly start finding them stuck in your tender inner arms. If you get glochids in clothing you can find them (the hard way) for weeks after. Do NOT, I repeat do NOT try to remove spines by running the clothing through the washing machine, or they can get redistributed throughout your laundry.

Pro-tip: if you order a cactus with glochids in the mail, treat the package like it is filled with satan's glitter and loose fiberglass. You do not want to be dropping and wafting loose glochids all around your house!

Maintain situational awareness

I once heard a professional at a cactus botanical garden explain the key to avoiding getting pricked: it's not the one you're working on that will get you, it's the one next to it. For example, when you're trying to remove a cactus pup and it breaks free so suddenly you whack your hand into the cactus next door. Try not to do that.

When I moved to Tucson I quickly learned to maintain situational awareness. Cacti are everywhere, even where you least expect it. I once found a piece of cholla an animal left on top of the back wall of my garden, and I've backed into spines more than once. I had to do a move out of The Matrix to avoid walking into a cholla branch that was hanging over the sidewalk one day because I was busy looking at my phone. 

I frequently fail to follow my own good advice which is how stuff like this happens:

Establish no-touch zones

Something with mean spines shouldn't be living somewhere where it poses a hazard. If you keep getting bit by a particular cactus, move it behind a buffer zone of less-aggressive cacti (if you can't move it, place a ring of pots around it). That way, you'll get a gentler reminder you're approaching the danger zone.

Appropriate handling

Gloves

Gloves will only go so far to protect you, and many store-bought gardening gloves aren't at all made to withstand spines. Cactus gloves exist, and are tough like dog-handling gloves. But if you've seen the Desert Worlds episode of Green Planet, you know even that isn't enough for some spines; the show features David Attenborough playing with cholla at Saguaro National Park here in Tucson!

I have not invested in a pair of cactus gloves. Personally I'm a klutz and find it easier to delicately maneuver and feel what I am doing without the bulk on my hands. Instead I rely on...

Tongs

When you need to directly handle cacti, like when repotting, kitchen tongs are a cactus gardeners best friend. I prefer the ones that are silicone-tipped so I can grab a cactus with force without sharp edges cutting into the flesh. I use tongs to handle the cactus when planting and repotting, and also to pluck small pots out from between cacti.

If you are working with little cacti, the kind of tongs or long tweezers used to feed reptiles work great! They have a bit of give so you can work with a lighter touch.

Cactus slings 

When you are working with taller cacti, use a piece of scrap material as a sling to move and carry it horizontally. Good options include a piece of carpet, burlap, old clothing, straps, or folded newspaper. I often use a scrap of weed-blocking cloth. Just don't use anything you are too fond of, since a lot of cacti will leave souvenirs.

It's too late for me, how do I get the spines out?

Glochids

When you are dealing with glochids, you want Elmer's or a similar flexible glue but in a pickle you can use other home remedies like hot wax, peelable facials, plaster, or duct tape.

Drizzle glue over the area and strengthen it by lightly patting in a strip of something flexible like paper or a plastic market bag. Wherever you think the spines are, cover a larger area because your mind will play tricks on you. Once the glue has fully dried, peel it off and if you're lucky all the spines will come with it. Spines that are barbed or barely sticking above the skin's surface can be tougher to get out. I recommend going in with magnification and tweezers—I use a jeweler's visor. 

If you're unsure whether you got them all, lightly wipe a piece of fabric across the area. Clothing that is a bit fuzzy and pill-bally like an old tee shirt is fantastic at snagging small spines.

Alternate method: I've had some success scraping spines off, similar to the 'credit card' method of removing a bee stinger but with more forceful scraping action. This does risk breaking off spines and leaving the irritating tips in your skin.

Even if you get all of the glochids out, you can expect the area to remain irritated for hours or even days. This is because glochids typically leave behind small barbs in the skin.

Larger spines

Pro tip: Have a segment of cholla stuck on you? Park rangers recommend using a comb to remove it!

Larger spines are easier to see and remove in most ways compared to glochids. Worst case with spines, you will bleed and need needle-nose pliers instead of tweezers. Just try not to break the spine off at your skin's surface or it gets harder to extract. Spines can snap off when you hit them so the tip is entirely embedded in your skin, and can't be felt from the surface. I had over a quarter inch of torch cactus spine inside in a knuckle for days and could tell because it felt like a nerve was getting lit up when I bent the joint wrong.

You may see a small black or brown spot or line under your skin after getting poked. Or you might feel like you are getting stabbed internally every time you put pressure on that spot. If it's not bothersome, you can leave it alone and let your body reject it over time (this means forming an itchy blister or small sore). Sometimes your body decides to form a pearl of scar tissue instead though.

You may be able to work spine tips out by pinching the skin under it, creating pressure pushing/pulling toward the skin's surface. You may get the spine to stick out enough to grab it with tweezers. If that doesn't work I get impatient and slice the skin open to expose the spine. Just be safe and sterile if you're going to act like a caveman.

In conclusion