I thought I would offer my experience as a guide for beginners to level up.
Its really not that hard. I have found the quickest way to level up, at least for federation characters, is through exploration missions. Captain 1 to 3 in under 2 hours. 155 skill points per mission, plus turning in the triplet for an additional 155.
The benefit of this over other ways is that you also gain exploration merits which you can use to either gain some decent gear from the requisition officers, or gain gear and sell it on the exchange or to an npc/replicator to buy specifc stuff from the exchange you can get through converting your merits to items.
Its also a great source of anomolous data for crafting.