Train
There is one daily train from St.Petersburg to Velikiy Novgorod and return.
Timetable (subject to change):
Train #801 St.Petersburg 17:18 - Novgorod 20:33
Train #802 Novgorod 08:05 - St.Petersburg 11:25
2nd class seats are available.

Daily train #042 connects Moscow and Velikiy Novgorod.
Timetable (subject to change):
Train #042 St.Petersburg 21:50 - Novgorod 05:50
Train #042 Novgorod 21:20 - Moscow 05:32
1st, 2nd and 3rd classes are available.

Velikiy Novgorod is connected by rail with: Murmansk, Petrozavodsk, Minsk, Kishinev etc. All trains arrive/depart to/from Novgorod train station.

Bus
There are about 10 daily buses between St.Petersburg and Novgorod.
Timetable of regular daily buses (subject to change):
St.Petersburg 07:30 - Novgorod 11:00
St.Petersburg 09:30 - Novgorod 13:30
St.Petersburg 10:35 - Novgorod 14:25
St.Petersburg 13:00 - Novgorod 16:50
St.Petersburg 15:30 - Novgorod 12:20
St.Petersburg 16:00 - Novgorod 19:30
St.Petersburg 16:30 - Novgorod 20:40
St.Petersburg 18:00 - Novgorod 21:40
St.Petersburg 19:50 - Novgorod 23:40
St.Petersburg 20:35 - Novgorod 00:10+1
St.Petersburg 21:30 - Novgorod 00:55+1

Novgorod 05:35 - St.Petersburg 09:20
Novgorod 06:30 - St.Petersburg 09:55
Novgorod 07:00 - St.Petersburg 11:10
Novgorod 08:50 - St.Petersburg 13:00
Novgorod 12:00 - St.Petersburg 15:30
Novgorod 14:30 - St.Petersburg 18:20
Novgorod 16:00 - St.Petersburg 20:00
Novgorod 16:30 - St.Petersburg 20:20
Novgorod 18:30 - St.Petersburg 22:20
Novgorod 20:05 - St.Petersburg 23:35

From other cities.
Novgorod is connected by bus with: Pskov, Tver, Riga, Staraya Russa, Luga, Valday, Malaya Vishera etc. All buses arrive/depart to/from Novgorod bus station (next to the train station).

Car
From St.Petersburg.
Riding 180 km from St.Petersburg to Novgorod takes about 2-2.5 hours.
There are taxis near Novgorod bus station which can be hired for this transfer.

Transfers
Railway Station - Hotel or vice versa:
23 Euro per car (up to 3 persons).