I'm also only new to the game but I've found that the Brutii can build temples to mars which provide units 1, 2 or 3 chevrons of experience as soon as they are constructed where a temple is built.

Overall however I have no idea how experience points are dished out after battles. I've had units perform brilliantly and literally save the day yet another unit which did very little in the battle received exerience. The only thing that seems to make a difference IMO is how well you win the battle; i.e. in cases of "heroic victories" I find that more experience points are given than in the case of a "clear victory".

In any case, use those gold Hastii as much as you can, I find them be as deadly as noob earily legionaries or even legionary cohorts if they have 2 or 3 gold chevs!