The new arena mode is fairly complex, there will be some in game instructions to explain how everything works, in the meantime please consult the following text to understand the basics.
You will start in your base of operations. For now there are three main things of interest here: a shop, a roster and a match board. The roster and match board appear as notices pinned on wooden boards, click on these to open them.
ROSTER
This is where you can view and manage all your characters. Select a character and click manage or simply double click them to get a detailed view.
When managing a character you will see their match loadouts, their inventories, an arsenal where you can store and manage all your gear and their skills.
Your character will progress a rank for every two skill techniques trained. A higher rank will give you access to higher rank matches in which you can use higher rank equipment. There is an equipment loadout per rank, even when you achieve a higher rank you can still participate in matches with reduced equipment ranks and the corresponding loadout will apply. Every rank also has a point limit towards which every piece of equipment contributes.
RECRUITS
Recruits are additional player characters that you can control yourself during matches in place of your own. It is useful to cycle between characters so that the others have time to heal. When a character suffers full red damage during a figh they will die and be lost forever, if this is your main character you will lose everything.
MATCHES
The match board is where you can view and choose what matches to participate in. Select a match and then enter characters into it by dragging them into the space on the bottom right, then click "Enter" to begin the match.
Characters must meet the rank requirement of the match to enter. This rank is also indicative of what rank equipment is allowed in the match. If the rank requirement is suitably low, you can enter higher tier matches, these however feature more skilled and experienced fighters, but also award larger prizes and provide faster training for your skills.
Be careful entering high tier, low rank matches as these can be the most deadly, also challenger matches which are devoid of rank restrictions. Elimination matches work similarly to the old arena, but with five consecutive fights and no red bar healing inbetween. These present a very tough challenge but also great rewards in prize money and experience.
THE SHOP
This is pretty self explanatory really. Drag items you want to buy from the shop's stock on the centre right pane, items you want to sell on the left. The paperdoll on here is so you can try items on and view them before you buy them.
Invest your money wisely and as early as possible, even basic clothing can offer much needed protection and all rank gear is useful throughout the game.