Well the first engagment happened on the right of the royalist line, when dragoons fired upon royalist horsemen through hedges, those horsemen charged the Parlimentarian cavalry in front of them, though they won and drove them off the field, the Royalists found the supply and baggage wagons, they began looting the baggage and would take no more part in the battle.
In the centre, the Royalists had 3 lines of infantry In a pyramid shape, the rear infantry were the reserves, the front two lines advanced upon the Parlimentarian New Model army and they clashed, the Royalists at first were getting the better of the fighting and Parlimentarian troops were starting to flee.
It was then that Cromwell with his Ironsides on the right of the Parlimentarin line decided to charge the enemy cavalry in front of him in order to save the centre, the Ironsides overthrew the Royalist horsemen, some men were sent to keep them routing while the rest charged the Bluecoat infantry in the centre. This charge, and reinfocments for the Parlimentarian in the form of fresh troops and rallied men defeated the Bluecoats in the centre.
The reserve Bluecoats were the ones who performed the heroic last stand mentioned, from what I understand, theu kept their pikes up at surrounding cavalry to avoid being charged while the matchlock men fired, I don't know my knowledge on Naesby is limited.
In terms of Royalist tactics, I suppose having one reserve and attempting to crush the Parlimentarian with the front two ranks, otherwise I don't know.
Thats more or less all I know about Naesby, could find out more, hoped it helped, best of luck