The best way to learn a new game kind of depends on whether you are running a game or playing it, there is some overlap, but there is a much greater onus on the person running the game than those playing it.
Starting with playing, I honestly believe you can just show up and have the DM walk you through the game, starting at CharGen and working through to a very simple adventure that highlights the key components of the game, usually combat, exploration, social interaction and skill challenges.
Personally, as a player I like to get copy of the rules of any game i’m going to play, ahead of time, so I can familiarise myself with CharGen and the rules that are likely to be applicable to the type of character I want to play.
As a DM I think the job is harder. The job of the DM is to learn pretty much all of the general rules of the game and be able to walk the players through the system. Thats not to say that the DM need know all the rules straight away (if ever really) but they should know all of the basics so the game can run reasonably smoothly and then they should note down any additional questions to check between sessions. In most cases, between those first few sessions, the DM will likely have a fairly long list of questions but as the campaign develops it should dwindle to nothing.
Personally, I also like to get a pre-written adventure when I’m learning the game, one written by the games designer preferably. This lets me understand how the game is intended to be run and played and helps me understand how to create my own stories within the framework of the game. I know a lot of people frown upon pre-written adventures but they are something that I find to be a great resource, even if I never run them.
At the end of the day, learning a game can be a painful process, especially if it’s a complex system, like Shadowrun or Alpha Omega, but as long as everyone is on the same page, forgives mistakes and are willing to adapt to week by week changes in how the rules are interpreted until things get settled, then it can be a very rewarding and exciting change from the norm.