How did they rack up so many deaths in a short period of time?

Just on this point - the number of casualties was high because the number of men involved was high.

The actual casualty rates were not historically unprecedented, having been frequently exceeded before and since (At Waterloo, casualty rates for the French and Coalition were 60% and 20% respectively of the entire armies and in a single day of operations). It was the scale of operations that was unprecedented; never before could armies of millions of men be kept actively in the field indefinitely.

The number of casualties appears particularly egregious from the British perspective because this was the first and only time a British army would take the role of the main combatant, engageing the main body of the main enemy in the main theatre of a general European war.

Was there a specific strategy in evading casualties when doing these human wave charges?

I just want to deal with this phrase 'human wave', specifically, with this paper on it. To quote the work:

A human wave attack is a pejorative term for an attack by massed infantry on a defended enemy position, intended to overwhelm the defenders by sheer weight of numbers and regardless of inevitable high casualties. The term implies both a lack of tactical subtlety by the attacker, and the defender's ability to inflict horrific casualties on the defender, usually through superior firepower, training or technology. It also suggests a callousness of the attacker towards its own troops, and therefore the term is likely to be used only by the defender or a later commentator; it is doubtful whether any attacker has ever used the term, or whether it has ever appeared in a tactical manual. Human wave tactics would normally only be used by an attacker who lacks firepower and the ability to maneuver, but whose main advantage is in numbers of men. His men may be poorly trained, though highly motivated: great physical courage and esprit de corps is required to advance unflinchingly into superior enemy fire.

I firmly do believe that 'human wave tactics', as explained by the author of this, have not existed nor have they been used in any concrete way. It's a pejorative term first and foremost and it's something I really wanted to bite into the bud. Yes, there were humans. Yes, they were generally sent in 'waves' of reinforcements. Yes, there were tactics involved. That does not mean human wave tactics in the common definition.

How did they rack up so many deaths in a short period of time?

Seems I'm working backwards here. So many deaths in a short period of time came mostly from artillery and pre-bombardments. Something of 72-75% of all casualties in the war were via artillery and most artillery came directly preceding an attack.

When they went 'over the top', were they setting up skirmish lines and just having a shoot out with the other side? Were they attempting to actually get into the other trench and start shooting people?

The answer is...'it depends'. Generally, both. You'd fire on the enemy positions to suppress them while advancing with the ultimate goal of reaching the enemy trench as fast as possible and getting in it with them. Rifles would become clubs, trench knives would be pulled, pistols fired, other forms of clubs and daggers and even hatchets would be used to whack people in what was basically face to face combat. Men would try to hold chokepoints with machine guns when they could but considering the zig-zag nature of trenches along with their claustrophobic nature that became difficult. Flamethrowers and gas would be used to empty out extremely fortified positions or to clear out entire lines of trenches as well.

We can generally say though that in '15 and '16 it was about hitting their trench as hard and as fast as possible with less lolly-gagging around in no mans land. The plan was to obliterate their defenses, get in there, clean up, and secure it. Later '16 and '17 saw a more fluid form of warfare arise where men would actually engage more in no mans land in the remains of craters caused by artillery. This image comes to mind when I think of this period of the war. It was denoted by a massive use of grenades, personal mortars, and lots and lots and lots of grenades. A lot more fluid warfare in my opinion and the beginnings of more lower level squad based tactics.

1918 would see the true form of what '17 was beginning to become. Both sides by Summer would be using squads of elite troops whose purpose would be to firstly infiltrate the enemy trenches directly preceding an attack and more importantly to strike immediately, as in seconds, after the artillery bombardment finishes. The hope was that as the men were crawling out of their holes after the bombardment to man their weapons these elite troops would already be upon them along with the men previously infiltrated hitting them from all sides specially armed for close combat. These were, for the Germans, called Stoßtruppen, or Stormtroopers. The Russians were actually the first to do this in 1916 (whom the Germans likely got some experience from) and the British were widely implementing these ideas in 1917 as well. After this infantry would advance generally with the cover of armor. The hope was that when the Stormtroopers seized the weaker points of the trench the 'regular' troops could hit the strong point and the Stormtroopers could hit the strong points from the 'sides' and 'behind' and generally make the strong points not so strong anymore.

TL;DR:

The ultimate issue is that, especially for the British, there never really was any ubiquitous doctrine of how to carry out assaults. It just depended on who was in charge. However we can speak in broad strokes. Further it was generally not the effectiveness of the infantry but the artillery bombardment that determined the success of an attack, especially in 'Winter '14 - '17.

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Further reading:

Hot Blood and Cold Steel: Life in the British Trenches in the First World War by Andy Simpson

Tommy: The British Soldier on the Western Front by Richard Holmes

The Kaisers Battle by Martin Middlebrook