One approach to maximizing spell casts for a minimum amount of effort would be to build a deck with the following cards:
1-4x Cloudshift (White; Battle Booster)
1-4x Archaeomancer (Blue; Shandalar)
Many White land cards (basic, gates, triples, etc.)
As soon as you draw an Archaeomancer, cast it onto the Battlefield. As soon as you draw a Cloudshift, continuously cast it on the Archaeomancer; when the latter card prompts you for a card to retrieve from your Graveyard, select the Cloudshift. As your mana pool grows, the number of times you can recast Cloudshift per turn should also grow.
The above process can take some time to get running, so augmenting the deck with cards which allow you to draw or sift through your library can be beneficial. The following are some suggestions, but not hard requirements:
Quicken (Blue; Ravnica) (1x draw)
Void Snare (Blue; Shandalar) (Return card to hand)
Quickling (Blue; Shandalar) (Return card to hand; useful for redeploying Archaeomancers)
Ior Ruin Expedition (Blue; Zendikar) (Landfall powered quest card; 2x draw)
Voyage's End (Blue; Theros) (Return card to hand)
Think Twice (Blue; Battle Booster) (1x draw)
Inspiration (Blue; Ravnica) (2x draw)
Species Gorger (Blue/Green; Ravnica) (Return card during upkeep)
It might help to do this in practice mode against a dummy deck: one which has mana cards of an incompatible type with the mana requirements of its non-land permanents. Such a deck should be unable to ever cast anything to disrupt your casting process.