Alnwick is a relatively small market town North of Newcastle, so public transport links are good (if occasionally a little pricy!)
By Train:
Both LUMO and LNER run trains from London to Edinburgh, stopping at Newcastle.
Both are cheaper if you book in advance, but only open tickets approx 12 weeks ahead of travel.
From Newcastle, the CrossCountry service to Glasgow Central will take you to nearby Alnmouth, after which a short bus journey will bring you into Alnwick itself.
By Bus:
National Express run services from London to Newcastle, and then from Newcastle to Alnwick, with prices starting at £39 per adult for the whole journey in one direction.
By Car:
Perhaps the most convenient method for most (especially those of us based in the South!) will be to arrive by car. The gardens has plenty of parking on-site for the day.
Alnwick Castle and Garden share a large car park, and will appear on google if you search. For sat navs, the postcode is NE66 1HB. There will be some free parking available in the accessible car park, but if this is full when you arrive then you may need to park in the main car park at a cost of £3.50 for the day. We will provide more details when we have them.
Please note: the Castle is a separate attraction, so unfortunately entrance to this is not included but you are of course welcome to visit any time, including the morning prior to the wedding.
Being a relatively small town it may well be feasible to walk up to the gardens from your hotel/b&b/cottage and leave the car there instead (there will be a bar available throughout the day, so this may be a sensible option).
There are also several local taxi firms, who will be happy to ferry you back to your accommodation.