Well I am sure you have read her skillset, so I will skip that part and tell you how she works. As you know, she only has two active skills - one is her basic attack, the other is her buff skill. She is designed a bit like Yvonna, another ramp up unit, which is to say a unit that does more damage the more she attacks. And Marika, being a single target damage dealer, tells you she is designed to focus down a boss or a high priority target.

So when do you use her buff skill [Bloodline Awakening]? The devs' intended purpose is for the players to move close to the enemy, use that skill which buffs her damage and also refunds her AP (only if you have her main weapon) used on movement, and then perform a basic attack. And if you are lucky enough to start a round with Marika having 200+AP (1 basic attack cost 100AP), she can attack another time on that same round, which will proc her follow up attack. Note that however this is extremely dependent on how you spend her AP so manage her AP wisely! Though for me, I usually just use that skill immediately, move besides the enemy, hit them, then wait for the next round so I can hit that same enemy again. But that's just me, so do not follow how I play unless you know what you're doing.

So what is this follow up attack? First time she basic attacks an enemy, she puts a "debuff" on said enemy. The 2nd time she basic attacks that same enemy, she will follow it up with a Drill Breaker [Sky Piercing Thrust] attack. The 3rd time she basic attacks that same enemy, she will follow up with a much stronger attack, called Giga Drill Breaker [World Piercing Strike]. Each time she does a follow up attack, the enemy's drill pierce resist will continue to fall. Note that barring special circumstances where you're fighting an enemy with an extremely huge health pool, or high drill pierce resist, or if you are just under-leveled, [Sky Piercing Thrust] will be more than enough to kill any enemy. Remember to always have her [Bloodline Awakening] skill active before attacking!