After selecting the battle format that you're making your team to battle in, you will want to hit the “+ Add Pokémon” button shown in the 1st screenshot above, and then either scroll down through the list of Pokémon that is shown and pick from those or (more likely) just search for the Pokemon that you want to add to your team.
(You can even search for Pokémon of a specific type, ones that can get a certain move or Ability, etc., etc.)





Once you've selected your Pokémon, the first thing you will need to do is pick their held item. Certain Pokémon (like Primal Groudon and Primal Kyogre) will require a specific held item for things like Mega Evolution, Primal Reversion, etc. After selecting a held item, you will then need to select an Ability for your Pokémon. Some Pokémon have only 1 option for an Ability while others can have as many as 3. In the case of Mega Evolved Pokémon (like the Mega Rayquaza above), you will need to select one of the Abilities that they can have prior to Mega Evolving, and their Ability while automatically change to their Mega Evolved form's Ability upon you Mega Evolving them in battle.



Next comes selecting your Pokemon's moves. Which moves a Pokémon can learn can vary dramatically from format to format, since new moves are added in each new generation of Pokémon games, some moves are removed each new generation of games (ever since Gen 8 anyway), and many battle formats have restrictions about which moves are allowed in them.as well. Thankfully, the National Dex Doubles Ubers format is VERY loose, allowing for Pokemon to use moves from their movepools in any generation of games.
(Including moves that they could only know as a result of being acquired from special events, like Rayquazas that know the move V-create.)



Next comes setting your Pokémon's stats. If you're new to competitive Pokemon battling this will likely seem confusing, but basically, the only things that you need to pay attention to here are your Pokémon's EVs and their Nature.

You get a total of 510 EVs to put into whichever stats you want, and you can put up to 252 into any 1 stat, meaning that if you max out 2 stats like Attack and Speed you will have 6 EVs leftover to add a tiny bit extra into a 3rd stat.

How you should allocate your EVs will depends entirely upon which Pokémon you're using and how you want to battle with them, but just know that every 4 EVs in a stat equals 1 extra point to that stat.

The other thing to adjust in the stats screens is your Pokémon's Nature. Your Pokémon's Nature will increase 1 of their 6 stats by 10% and decrease a different stat by 10%, unless you leave them with a neutral Nature like Serious that doesn't affect their stats at all.
(Just like EVs, which Nature you will want will vary greatly depending on the Pokémon and you're preferred battling style/strategy.)



Finally, after setting all of your Pokémon's stats you may want to set their “details”. I can't really do much with my Mega Rayquaza here since Rayquazas from the special event that had the move V-create couldn't be Shiny, and Mega Evolving Pokémon can't Terastallize.
(FYI, by “Mega Evolving Pokémon” here I actually mean those holding a Mega Stone, Rayquazas that know the move Dragon Ascent, Groudons and Kyogres holding their Primal Reversion orbs, AND any Pokémon holding a Z-Crystal.)

Still, as you can see here, you can set your Pokémon's gender here (for Pokémon who have more than 1 gender option anyway), their Shininess or lack thereof, their Tera Type, the type of their Hidden Power in case you wish to teach them that move, and of course, their level.
(Most formats on Pokémon Showdown use either level 100 or level 50 Pokémon, BTW.)



Once you've done all of this, you can go back to the page for your team of Pokémon by hitting the “< Team” button. From the team page you can give your Pokémon a cool nickname like I'm doing here. Afterwards, you will want to add the rest of your Pokémon to your team by going through the same process you went through to add your first Pokémon.



OK, now that I've got a full team of Pokémon to battle with, I need to validate my team to make sure that every Pokémon on it is allowed in the battle format that I chose.



Uh oh! It seems like there's a problem! It's saying that my Eternatus breaks the rules because their IVs (the thing I had y'all ignore in the stats page earlier) in their Attack stat are set to 0, and the only legitimate Shiny Eternatuses that exist in the actual handheld games are ones from a specific special event, and all of the Eternatuses from this event are supposed to have max IVs in everything.



The solution here is simple, however: I simply need to adjust my Eternatus's IV in their Attack stat to 31 instead of 0.
(Normally if a Pokémon knows no physical moves you would want it to have 0 IVs in Attack BTW, but that's unfortunately not an option here.)



As you can see now, after that 1 small adjustment, my team is now eligible for the National Dex Doubles Ubers format!

OK, now here are a few things to keep in mind when making a team for this Pokémon Showdown tournament of mine.

1. The National Dex Doubles Ubers format is a Double Battle format, meaning that both you and your opponent will be battling with 2 Pokémon out on each side at a time.

2. I chose this particular battle format because almost everything that can be legitimately acquired in any Pokémon game is allowed in it. If your team was rejected for some reason, that means that it has at least 1 Pokémon that couldn't actually exist in any of the handheld games on it.
(Such as my Shiny Eternatus with 0 IVs in Attack, or a Magikarp that knows the move Dragon Ascent.)

3. Showdown gets a bit weird if you don't set your Pokémon's EVs. There's absolutely no reason not to anyway unless you want to battle with unnecessarily weak Pokémon, however, so you should just allocate your Pokemon's EVs.
(Rest assured, you will lose if you don't, lol!)

OK, let's suppose that rather than trying to come up with a team of Pokémon you'd rather just use a cool one made by someone else. If so, you'll want to select the “Import from text or URL” button here.





Once you're in the screen shown in the 1st screenshot above, simply copy the team of Pokémon that you want to use and past it into the textbox here, like I did in the 2nd screenshot above, and then hit the “Save” button.





As you can see, I now have a full team of Pokémon ready to battle with. Imported teams do still need to be validated since the rules of the different formats change sometimes, but in general, if you import a team from an experienced Pokemon team maker (like myself), it saves you a TON of effort struggling to come up with one on your own.

Here are a few National Dex Doubles Ubers Teams I came up with a while back for people to use in my tournament. If you don't want to try to come up with your own team, feel free to use any of these ones.

You can change your avatar on Pokémon Showdown in the settings, but there's an even better way to do it, that gives you far more avatars to choose from than picking one from the settings menu does: the /avatar command.







To use it, simply hit the profile icon (the blue thing in the top right in the 1st screenshot) to bring up your Pokémon Showdown profile. Then, hit the “Chat self” button shown in the 2nd screenshot above. Finally type /avatar *name of Trainer sprite you want* into the chatbox. For a full list of Trainer sprites available for use as avatars on Pokémon Showdown and the names needed to be entered to use them, see this list here.