I'm making a two tiered shamrock cake and I've only made one other cake before so I'm still very new. Is it easier to cover the sides with a strip of fondant first and then put a top piece on and join with the sides?

I'd roll it out and cover the entire cake with one piece. Doing it in pieces leaves seams that are hard to get out. If you can do it in one piece, it's always best (IMO) to do it in one piece.

definetly go with one large piece of fondant, always roll it out larger than the cake and take in account the depth of your cakes so that the fondant will reach along the sides. i always measure lenght and depth x2 and then add a buffer of 1-2 more inches just to be on the safe side. hth if sometimes seams happen (i do alot of carved cakes) the best way to try and blend them is with a little bit of water and run your finger over it to rub it out.