As part of a couple inviting a third over, you'll probably feel some nervous anticipation about this whole concept. If it's your first threesome with your current partner, the idea of someone who isn't them is exciting, alluring, and scary all the same. For this reason, before you even begin thinking about the logistics of a threesome, both of you must set your boundaries. Do this in a non-sexual space – e.g. in the kitchen over dinner, whilst sober and allowing yourselves time to reflect afterwards for days before any action is taken.
Your boundaries – what you are and aren't OK with – will be unique to you as a couple. Discuss what you're both comfortable doing with your third (e.g. kissing, touching, oral sex, penetration…) and do not proceed until you are both on the same page. Don't forget to discuss protection and safe sex, and consent – what you'll do if one of you changes your mind when a threesome is pending.
Threesomes are intimate. Having one with a friend is, in my opinion, a good way to begin if you're part of an existing couple (picking up a stranger at a bar for a three-way isn't actually that easy). With a friend, you already have a level of trust to build upon. Naturally, you do risk screwing up the friendship, so it's important to do this right.
As the couple, I don't think it's wise to initiate. Your potential third party should be someone who has been flirty with both of you, and you've received the vibe that maybe they're interested. Maybe every time you see them at a cocktail party they subtly touch your forearms while talking to you… you'll feel it when it's there. They must come on to you first. Doing it the other way around can feel predatory.
Ask yourselves how sure you are that the potential third, your friend, is actually interested in both of you. Just a 50/50 chance? I would be hesitant in proceeding. If you're 80 per cent sure they are into you, go for gold.
Drop hints about being sexy together and wait to see if they are reciprocated. If the potential third is hesitant or uncomfortable, back off. Preserve the friendship and don't take it further.
I find the best locations for these sorts of interactions are small at-home gatherings where the libations are free-flowing, and everyone is at ease, so you can both build up the confidence to drop these hints. These events also allow you to laugh off a failed attempt at a threesome invite as a drunken mistake.
When you have a good amount of certainty your friend is game, you can go ahead with verbal and physical indications that you're interested in them sexually. Use the same techniques that work for you as a single person trying to pick up another. Everybody has their own unique pick-up methods.
If your threesome is going to happen, you'll be sure of it before you ask. But, you still need to be upfront and actually ask.
I find a polite and direct, "no pressure, but we both think you're really sexy and would like to take you home tonight" sort of approach works best, always caveated with, "no worries if you're not interested and we've gotten this wrong". If you're a heterosexual couple, it's also less intimidating for the person with the same gender as the potential third to do the asking (e.g. a woman invites another woman to sleep with her and her male partner). It's far less unnerving for the third.
If they respond positively and with levelheadedness, you have your first real go-ahead, but you need to offer the potential third some "outs" before they're actually in your bedroom. Respect any hesitancy to get in an Uber with you both, or to take you up on an offer of a nightcap at your place. There is risk in asking a friend for a threesome, and that friend needs to know they are the one in control.