Other than the Imperial Palace East Garden, which is open daily, the Imperial Palace Grounds are open to the general public, via Nijubashi Bridge, only two days of the year: on the Emperor’s Birthday (Dec 23) and New Year’s (Jan 2).
On both occasions, after completion of a security check, each visitor is given a paper Japanese flag and passes across the 19th century stone bridge and the Nijubishi Bridge behind it to gather in a large courtyard outside the Imperial Palace itself, a building constructed in the 1960s. The emperor and several members of his family appear on a glass enclosed balcony at fixed times throughout the day and the emperor delivers a short, formal greeting to the crowd, which responds by waiving the Japanese flags. The crowd is then escorted down a slope to exit via the Kikyo-mon gate. Unfortunately, the visit does not actually include an opportunity to enter the Imperial Palace.
On Dec 23, the emperor will appear three times, at 10:20 a.m., 11 a.m. and 11:40 a.m. There will also be greeting books available just after the security check points for well-wishers to inscribe greetings to him.
On Jan 2, the emperor will appear five times, at 10:10 a.m., 11 a.m., 11:50 a.m., 1:30 p.m. and 2:20 p.m.
On both days, it is wise to arrive in plenty of time, as it is usually crowded. Additionally, the gates close 10 to 20 minutes prior to the last imperial appearance.
It is also possible to make advance arrangements for a guided visit inside the Imperial Palace grounds (again, no chance to enter the palace itself). While these tours depart from Kikyo-mon and therefore do not pass over Nijubashi Bridge, otherwise visitors basically see the same things. For details on how to apply, see http://sankan.kunaicho.go.jp/english/guide/koukyo.html.