I'm a US Army Infantryman (though I've been a Tanker too) - I've been in uniform for 21 years, 18 of which were in the US Army & Army National Guard
US Army Marksmanship Training has evolved considerably over the past 8 years or so after being pretty stagnant for the previous decade or two.
New soldiers at the 10 week Army Basic Combat Training (BCT) progress through two phases of marksmanship training - Basic Rifle Marksmanship (BRM) and Advanced Rifle Marksmanship (ARM) with either the M4 Carbine or M16A4 Rifle.
BRM is ~73 hours of instruction. 5 hours classroom (fundamentals), 16 hours simulator (EST2000), and 52 hours live fire. Between live fire blocks, Soldiers needing remedial training return to the simulator before firing live again. All BRM live fire is with iron sights, and consists of 25m grouping & zeroing, known distance range, a field fire, 2 practice record qualifications, and final record qualification.
A recent change is that all BRM at BCT is fired without gear (except for eye & ear protection of course) - the Army found that it's easier to teach fundamentals minus all of the battle rattle.
The record qualification is 40 rounds fired on type F and type E plastic "pop-up" targets. Typically each Soldier is given a 4 10 round magazines. The first 20 rounds are fired from the prone supported position (sandbag for support). 20 targets from 50m - 300m present in single or double arrays in a marked firing lane. Targets stay up for a predetermined period of time, then drop back down. The closer the target, the less time it stays up. Targets are engaged as they present. Magazine change is conducted as needed by the Soldier. Hit targets drop, and hits are recorded by a computer. After the first 20 rounds a fired, the Soldier transitions to a prone unsupported position, loads the 10 round magazine, and is presented with 10 targets. Next the Soldier transitions to a kneeling position, loads the final 10 round magazine, and engages the last 10 targets as they present. Limited alibi fired are allowed for serious mechanical malfunctions observed by range cadre. Minimum qualifying score (Marksman) is 23-29 out of 40. Sharpshooter is 30-35. Expert is 36-40.
All Soldiers assigned a weapon are required to qualify annually, though many combat units qualify twice a year. Typically they will alternate between qualifying with iron sights, then with assigned optic M68 CCO, ACOG, EOTech, etc...
Advanced Rifle Marksmanship at BCT is ~28 hours. 6 hours simulator, 8 hours classroom, 14 hours live fire. ARM includes training with optics, and IR laser (PAQ-4) reflexive fire and night fire. All ARM is conducted with all battle rattle (body armor, LBV, etc.)
Certain military occupational specialties (infantry, cav scouts, combat engineers, MPs, etc) receive additional advanced marksmanship training at their schools, including various live fire exercises (mostly CQB stuff these days).
Combat units in particular continue intense marksmanship training, particularly when preparing for deployments.
I've done all kinds of reflexive firing drills, transition drills (rifle to pistol), failure drills, off hand shooting drills, etc... A lot of it is up to the resources and creativity of your unit.
The US Army also offers advances courses like Sniper, Squad Designated Marksman, Close Quarters Marksmanship and Close Quarters Squad Designated Marksmanship. I won't go into the details of those for obvious reasons....
Adrian