Wanted to try and revive this thread bc I think it provides a great prompt for people not only for building in adv, but also building in general. I posted in the advcord that everytime I build w someone else, I realize how little I know about a tier I've been playing for the last 10 years and played on console when it came out (holy shit im old). Seeing how those heuristics bear out is the one of the cool things about competitive Pokemon. This is also just my perspective: there are many great ADV builders out there who see the tier much differently than I do.
EDIT -- I finished this up.
tl;dr take an idea you have, try to look for other teams already used you enjoy to see if you can replicate something, and then have a heuristic if you handle major threats. Above all, test to see how your team performs in real games to see if works. Repeat to strengthen the team.
ADV is one of the most balanced gens in competitive Pokemon. Generally when I build, I typically start with what style I want to build. I am very influenced by the old Borat guide (the last iteration seen
here) where all of my teams have to have some kind way of making progress. I would define most of my teams to be of the style "aggressive stall" in terms of being able to switch into major threats (the big three to me are a rock resist, offstar check, and heracross check, but there are others like being able to limit Skarm's spikes, prevent celebi from passing cm/sd, having at least one pokemon not affected by spikes, etc) while also having a gameplan. What that gameplan is depends on what I want to use: there are many, but some examples include spikes, trapping, set up spam, etc. Even my most dedicated stalls have a way of winning beyond PP stalling (but are not afraid of that).
How to accomplish that depends a lot on the style. To take an example, let's start if I want to build w cm rest suicune + dugtrio. From here, I generally think of what metagame factors limit that idea. Suicune has poor recovery exacerbated by being phased while asleep, is passive until it gets multiple boosts, is affected by spikes, and generally struggles to break through bulky grass types, electric types, and physical water/dragon types. Dugtrio traps dangerous threats to suicune like tyranitar and metagross while also potentially resetting the weather while being vulnerable to giving reverse set-ups or traps. So then where do we go from here? First, I like to figure out what kind of direction I want to go w for the team -- Will I go in an aggressive direction like this team I used against teclis last
week :

(skeleton import
here) or will I try something more bulky a la this
team mcmeghan used in adv cup:

.
Since I built that first team, I can go through the teambuilding process and then extrapolate any overarching principles I use when I build. I wanted to go in an offensive direction against teclis. Once I decided that, I look to some more public replays to see what I can glean from what's already out there. Suicune + Dugtrio is a pretty common piece of a core; there are many viable version out there, but one place to look at is the zoomer classic

that was spammed throughout callous invite and was popularized by fear (iirc, I know zom had a hera version that I first got the original from). This team has a lot of synergy: Zapdos + Dugtrio helps remove threats for jirachi and suicune, jirachi + breloom + suicune + dugtrio in theory is enough for rock resists and handling physical threats, tyranitar can pursuit gengar so gar spikes isnt as threatening; zap, a fast jirachi, and dugtrio is generally enough to survive against heracross for this kind of offense. However, from testing this kind of team out, I (these are known I just happened to notice them too) noticed some issues: bulky dd tar can be a real pain if it gets to +2 against zapdos or on dugtrio upon forcing out zapdos or jirachi. Zapdos is extremely hard to switch into long term. Suicune needs ice beam or else dd mence can be a real pain. It is difficult to force enough damage on swampert that jirachi's subcm tbolt/ice punch can break through. Gar will survive the pursuit and you have nothing to take a burn. I wanted to try and fix some of these issues when I built the team above and hope the offense I generate is enough to overcome the others. There is no such thing as a perfect team.
Firstly, Jirachi is an unusual lead. The idea here is that surviving rocks long term is difficult for zapdos + dugtrio teams, as either you sacrifice you zapdos (and your only ground immunity unless you use gar > loom and become even more weak to dd tar) t1 or you switch to loom/suicune (or pert) and take a huge hit. Jirachi tries to combat both the long term zapdos weakness by being specially bulky and toxicing it and the rock weakness by hp fighting ttar t1, which has good chances to 2hko a max hp ttar. Other special offenses like those that lead w jynx like to sacrifice it t1 to ice beam metagross and ttar leads -- you can do this too if you so choose and trap them. I got the idea to lead something specially defensive from the roro regice team seen
here. From here, the other unusual mon you see is machamp. Machamp is a specially bulky dd tar counter that switches in and a) ohkos gar w hp ghost while taking its hits well and b) is a viable option to subpass to. Another line you can try is to hard zapdos on metagross t1 and sub on the switch out. if they go ttar, your sub survives both crunch and rock slide, meaning you get a free focus punch. Machamp also is never ohkoed by ddtar without a crit, so you dont have to let your suicune or dugtrio be your only answer/can be slower or less strong to better trap other things. Going w machamp that answers gengar allows you to regain some of your sweeping prowess of spdef jirachi > subcm by going bulky lum ddtar > pursuit tar. It also gives you a back up answer to salamence in case suicune takes too much damage. You can select the rest of your sets accordingly: Suicune needs to have ice beam, or else your salamence answer is too weak, but also needs bulk/rest to answer rocks and swampert long term. How did i know these were all metagame factors I needed to address? I practiced a lot w both the archetype and the team.
From baring this out, generally what I need to see in a team I like are handling metagame trends in adv that i mentioned above (rock resist, offstar check, and heracross answer among others). I am in the bkc camp that i typically do not ignore threats in the teambuilder -- i try to be able to either out offense or at least have a check to everything in the metagame. My teams also generally always have a plan to the pace, whether thats spikes, a set up threat, trappers, sleep, etc. I also try to avoid having teams that are too grounded or I can't handle spikes long term. Some of these heuristics are complimentary -- heracross answers are generally not grounded, offstar checks can generally help you team survive long term against spikes, etc.
The idea phase is typically where I find myself negotiating mus. In the above example, picking your suicune and dugtrio set can help organize your mus. Will you choose a suicune set that better sweeps teams lacking bliss in full out offcune? Or will you try a cm rest variant that can handle metagame factors a bit better? Will your dugtrio be fat? Slow? adamant? Another way to do it is for example Charizard + Breloom as an idea. Charizard is very effective against bulky tss that lack suicune or milotic, whereas breloom is quite effective against non only sleep those, but also against more offensive teams zard might struggle w. I typically find myself emulating someone like altina (and by extension, astamatitos) and their builds a lot. The best way to improve your building is to get out there and try stuff!
Thank you for reading so far!