First of all, welcome to our forum! We hope you enjoy your stay.
You may be wondering what this is all about and what to do now that you're here. If so, you've come to the right thread.
First of all, you will need one or more pokemon. You can get adopted Pokemon at the Adoption Centers, and captured pokemon at the Captured Centers.
If you want an adopted pokemon, just go to either adoption center and look at the latest list of available pokemon. Then ask for one that hasn't been adopted yet and a worker will give it to you when s/he sees your post. If it's your first time adopting, you can pick a level 5 pokemon of your choice as your starter, as long as it's not evolved, legendary or Dratini (basic pokemon that have an optional baby form are allowed).
If you want a captured pokemon, post at a capture center and a worker will guide you. Note that Adopted Pokemon and Captured Pokemon are two different games. They're not compatible with each other.
Alternatively, you can request either and adopted pokemon or a captured pokemon to be bred for you. If that's what you want, go to Pocket Monsters Breeding Center and select the 2 pokemon you'd like as the parents from the available pokemon list.
You can get up to 2 adopted and/or captured pokemon per day. You can have up to 15 adopted pokemon and up to 15 captured pokemon, so choose your teams wisely.
You can give your pokemon a nickname, a bred-on move of your choice and a compatible ability. Your pokemon will also know the moves it would know by its current level on GSC (yes, GSC), plus any moves not available in GSC that it would have learnt in other games. This may seem convoluted, but it's less confusing than changing the moves each pokemon knows whenever a new game comes out. Additionally, you can get a free TM from any of the games whenever your pokemon reaches a level that is a multiple of 10.
Once you have your pokemon, you can start training them. There are two different ways to do this: you can battle other trainers at the Battle Tower with a battle system that resembles the games, or you can roleplay with them at the Battle Range (for adopted pokemon) or the Battledome (for captured pokemon). You're welcome to try either or both.
You should keep track of your pokemon and items at the database. You can either post all your info there or make a website and post a link to it. Just make sure to keep everything up to date.
There are places you can go to get items that can help you in your battles, as well as evolution items, TMs and juices to give your pokemon special colors. Make sure to check out the Reward Center (for adopted pokemon), the Kiosk (for captured pokemon) and the Goldenrod Tower (for both kinds of pokemon).
You will need stamps or Capture Center Points (CCP) in order to buy items and access some special features. You can get them at the Goldenrod Tower, earn them by writing good stories at the Battle Range or the Battledome, get them as a reward for helping other members, win them in tournaments or other games, or get them in trades with other trainers.
That's it for the basics. Beyond that, there are other threads you can explore. Make sure to read the rules and the FAQ. As a bonus, the rules thread contains a list of the active threads and what you can do in each of them. If you have any further questions, don't be afraid to ask.