The best advice I can give you for fighting Necrons is to not give up. It will seem like you're doing nothing and he's trouncing you for a lot of the fight but as the battle draws out you will eventually reach those magical thresholds (crippled/destroyed) and he'll be unable to afford to avoid to BFI. This greatly diminishes his firepower and therefore increases the value of your shields.
Apart from that, fire your WBs before your lances. If he braces against the WBs under the expectation of forthcoming lances then redirect those lances to unbraced ships. If he doesn't brace then at least your WBs will have had the greatest chance of causing damage and you can follow up with lances (which he may fail to brace against allowing for easier damage).
Spread your fire. Throw incidental shots in wherever you may. Make it hard for him to decide if it's worth bracing. Only focus fire when a ship is near a crippled/destroyed threshold. The exception being the escorts feel free to throw as much firepower into them as it takes, until they brace of course.
Your priorities should be to destroy/shutdown the escorts, then to destroy the Shroud, then to shutdown the Scythes. Try to avoid the Cairn as much as possible, don't focus fire on it, the occasional lance shot into it is fine. Focus on the rest of the fleet first.
As for manoeuvring, you'll want to put yourself behind the cruisers. If you can make him turn his ships in different directions you'll get best results, as Necrons really need to stick together. If he goes on AAF he'll typically end up getting split up due to the large variance in AAF distance. This is good. You can split your fleet in order to make him chase you and use your great speed to form up again later.
