How does one play as the Human Race?

Make sure to lvl avalon virion and vega.
Focus your research on 1.archers 2.swords/horses, skip all of the other units research and do not bother lvling up their building.

That is the core of playing human, if you have any more specfic questions feel free to ask.

Oh. Currently my army is core spearmen, and archer's. Why would sword's be a good idea?

Spearmen are ok in the begining. But there is no passive hero buff for them (Avalon- archers/ Virion-swords buff + ressurecting them/ Elena - calvary / Vega - priests).
So in the mid-late game you must switch to swordmen/calvary. As Destination said they become redundant after a while. I did use them long time (up to lvl 10-11) for bronze sieges to clean calvary in other human garrisons and they were better than swords with equal upgrades untill my Virion got leveled up. I doubt you can actually skip pikes so early (they are helpful for certain tactics school/void levels and are always level ahead) but try to focus on the research Destination proposed... For calvary you must buy Elena hero... otherwise they aren't that strong at least for me. I guess somebody can confirm from fresh realm experience at which point pikes become useless but my guess is after lvl 8. Or if the building can be skipped even earlier. Afcourse you need to spend good ammount money if you want to enjoy this "game".

Spearman are good vs large, but only for npc. In PvP you go with templars and you must have Elena with cav boost.

As per garrison lvl 13 are good if you invest in research, but swords are better.

so when ur starting out u just click avalon then 2x archer then 2x sword and 1xhorse , virion ofcourse and add 2 more horses if ur taking heavy losses .. this auto loadout will beat all map content without a problem.. passive bonuses on heros to boost most used troops and try save for elena/tiadrin/yipp .. maybe splurge on a jacqs if u really want him and ur good to go..