Start out simple
Infinity is a complex game, but the complexity comes in layers. For your first games, all you need is a basic understanding of the order/ARO mechanism and how dice rolling in fire combat works. Save things like hackers and lots of objectives for later games. Start out with a 150 point list with seven or eight troopers with a limited amount of special skills.
Print your list
Nothing is more annoying than having to look up unit statistics in Infinity Army all the time. Printing you list means that you have everything, including weapon stats, readily available. You can also print a courtesy list that doesn’t include points cost or hidden units for your opponent.
Prepare a cheat sheet
With so many special rules, it is easy to forget what exactly they do, and having to search for everything in the rule book or the Wiki is time consuming and hampers the flow of the game. Creating a simple cheat sheet with a short summary of the special rules that apply to your list can speed up things considerably.
Some rules to remember
Suppressive fire is an important mechanic, as it grants the unit a Burst 3 ARO (where normally you are limited to Burst 1 in ARO) and a -3 modifier to the opponent. You probably want most of your cheap Combi Rifle units in suppressive fire at the end of your active turn.
It can sometimes seem impossible to cross the firing lane of an enemy model. Don’t forget that Cautious movement lets you move through a model’s LOF, outside of its zone of control, without triggering an ARO. This may let you get closer to a sniper into a range band that is more favorable for you.
Don’t forget that Facing matters in Infinity, so make sure your models are oriented in a way that keeps them from being sneaked upon from behind.
Going Prone lets you hide behind low cover. When higher than the enemy, prone grants the partial cover bonus, so you probably want to go prone on a flat roof that otherwise provides no cover.
By spending a command token and a regular order, you may perform a Coordinated order, i.e. the same order with up to four units. Very useful for economically moving several units forward on your first turn, or putting more than one into suppressive fire at the end of your active turn.
Don’t be afraid to as the more experienced players questions. Playing against people with more experience, and asking why they did something that puzzles you or asking for advice or a rules clarification will speed up you learning the game.
Add complexity step by step
Once you’ve grasped the basics of the game, you can successively add complexity. Special rules (like camouflage, airborne deployment, etc.), hacking and fireteams can be introduced step by step. This will make the game much more accessible and easy to learn.