If you're coming from DC or somewhere else on the East Coast, we highly recommend Amtrak rather than flying. Tickets can be quite reasonable if you buy in advance, so get moving on that sooner rather than later. If you're flying in, any of NYC's three airports work, but LaGuardia is probably easiest if you're staying in Astoria.
Weirdly enough, Capital One has a pretty comprehensive guide: https://www.capitalone.com/learn-grow/more-than-money/transportation-to-manhattan-from-airport/ LGA is by far the closest if you're staying in Astoria, so a cab from the airport will be pretty reasonable. You can also take the bus; check Google Maps for transit plans from whatever airport you happen to be flying into.
Public transit is usually the best way to get around the city--Google Maps or the MTA's app both have solid transit directions, and the subway runs 24 hours. For getting around neighborhood destinations, bikeshare is also available, and it's a great way to see the city--the Citibike system will take you throughout Astoria, Manhattan and beyond.
The wedding is located at Irina's Dance Academy, 1219 Quentin Road, Brooklyn NY 11229. The best way to get there is via subway--the King's Highway stop on the B/Q train will drop you off just two short blocks from the venue. You can also take the N Train and get on the B82 bus. Sadly, the Citibike system hasn't extended that far south (yet!), so transit is the best way to go.
No need to bring anything but yourselves. Kids are welcome; please leave the pets at home unless it's a service animal. In terms of dress code: we invite you to dress comfortably. Please feel free to embrace flamboyance if your heart desires, but no need to be too formal--jeans and a polo/collared shirt, or your favorite caftan or sundress, would be fine. Don't think formal, think fun.