To get to work as a live sound engineer mixing top acts in big venues, you have to start as a trainee. You could set up your own PA system and work with local bands and try and scale things up from there, but you would learn at a much faster pace if you were working with people who already know what they are doing.
A small venue with a permanently installed sound system will probably require a roster of engineers. Sometimes bands will bring their own engineer, but often the venue will be expected to handle this. The venue will probably not employ engineers permanently, but hire them as and when needed on a freelance basis.
If you are not already skilled as a live sound engineer, you will need to gain experience by helping out. This can be on a formal or informal basis. Engineers will probably be very interested in having an assistant who will work for knowledge, and no money. The venue might have insurance considerations for people who work there, so it's best to formalize the arrangement if possible.
Working in a small venue will give you great experience with performers. But unless there are a number of venues where you can work, you won't get much experience with different sound systems.
A different approach is to work for a sound hire company. Major acts don't have their own PA systems these days. A system is hired for a show or tour, and the hire company will almost certainly supply the operators too, apart from perhaps the front of house and monitor engineers.
This can be on a much larger scale than a small venue, so you have to expect to start working lower down in the food chain. You would typically start by working in the warehouse. You will check equipment as it comes in, and prepare equipment to go out.
Building up and wiring amp racks might be one typical job. Repainting loudspeaker cabinets – they always get scuffed and scraped – might be another. If they get you sticking foam inside flight cases, well grin and bear it, but make sure you have plenty of ventilation for the fumes from the glue!
When you have shown that you are an effective employee, you will need to make it known that you would like to go out with the system. You will start by assisting with moving the equipment in and rigging it up (and of course de-rigging and moving out afterwards), then progress to increasingly responsible positions, finally – hopefully – ending up behind the front of house mixing console.