In crossfire the player with the initiative continues to move/shoot/whatever until he fails to accomplish a desired action when the initiative then shifts to the other player.
Moving is broken down into segments, a unit ends it's move when it enters a terrain piece. These 'moves' can be strung together so the same unit can keep moving but each 'move' is subject to reactionary fire from enemy units that can see the moving unit. Should the reactionary fire cause a result (suppress or kill) the phasing player's go ends and the initiative switches to the opponent who begins his/her series of manoeuvers etc.
Shooting follows the same formula, if you shoot in your go and cause damage you keep the initiative and can keep shooting and moving, fail to damage the target and lose the initiative.
There's a little more to it but that's the basics. The game revolves around decision making, what to try next and what
needs to be done. Moving stuff around in the rear, out of sight of the enemy, is risk free but everything that involves interacting directly with your opponent may, at any time, lose you the initiative and spark off a massive counter attack.
Sweeping flanking moves are a real and regular occurrence, in Crossfire you can't tell where a unit may move to, leave your flanks unprotected and suffer.
Crossfire makes you think more like an infantry commander and less like a gamer, if you lose badly it's generally your fault and you better lean from it if you want to win next time

Real tactics work and need to be employed in the game, fire and maneouver, pin and flank, position your commander so he can be a factor, remember to keep an all round defence and hold something in reserve to counter an unexpected move. Don't move around in the open and don't bunch up.
Although it's designed for WWII the system is so flexible that I use it for many different settings.
Crossfire is very simple to explain and I use it to run participation games at shows and to introduce new people to the concept of wargaming. there is no looking up on charts during a game and everyone has grasped the basics well before the end of their first turn.
When I first came across Crossfire I was amazed at how the simple premise worked so well. 'I want to move these troops over there' you think and off you go and do it. The
only thing that will stop you getting where you want to be is the enemy, just like on a real battlefield.
The lack of foreknowledge about where your opponent's troops can move to upsets some people, if it's going to upset you then find another rule set. Crossfire doesn't work well for multi player games either and requires a lot of fiddling to get something that works so if you want to play multi player, play something else.
If, on the other hand, you want a rules set that allows you to play a game concentrating on objectives and ways to achieve them that doesn't involve remembering 40,000 special rules that contradict the main rules and that only requires around 30 figures a side maybe Crossfire is for you.
My site is full of Crossfire stuff maybe you'll see something you like.
WWII:
http://www.matakishi.com/wwii19391945.htm
Weird WWII:
http://www.matakishi.com/weirdwar21939.htm
Modern:
http://www.matakishi.com/modernconflicts1950.htm
Sci Fi:
http://www.matakishi.com/futurewar2009onwards.htm
Currently working on Police drama too:
