What a sight! You've seen it a hundred times in pictures, but, as always, standing there in front of it is a real experience.
You can reach Buckingham from any of about a dozen roads that converge on it, but the best, in my opinion, was to start at Piccadilly Circus, hike down Piccadilly, then take the turn onto the Queen's Walk and approach from the side along Queen's Park, ending up at the Queen Victoria Monument and the Palace itself. It's a nice way to really feel yourself sinking deeper and deeper into the imperial history of the city as you shed the raucous, rowdy, and modern (Piccadilly) for the relative peace and tranquility, and history, of Buckingham.
The Palace is not tremendously impressive visually, to be honest. It is not all that architecturally ornate, but it IS massive. What really impressed me more, to be honest, was the Queen Victoria monument out front.
I was there in August, the height of tourist season, and managed to hit Buckingham in the midst of about 750 Japanese people. Now this isn't that uncommon in London, except that I speak Japanese. So, whilst standing by the Queen Victoria Monument, I overheard a Japanese family (mom, dad, and daughter) talking about taking pictures in front of Buckingham, and arguing about who should be in the picture, who should be taking it, etc. So, in Japanese, I mentioned that I couldn't help overhearing, and perhaps they would like for me to take a picture of all three of them?
In hindsight, my mistake was raising my voice from a slight distance away in order to be heard over the crowd of people. Next thing I know, about five or six VERY excited Japanese families have clustered around this gaijin (foreigner) who speaks their language, cameras and arms flying everywhere, anxious to not only have ME take their pictures in front of the palace, but then to have the father (always the father) dart out and shove me in with mom and the kids, so that they could take a picture with me. So, somewhere in Japan, half a dozen families have pictures of mom and the kids and some random American guy (yours truly) in front of Buckingham Palace. It took me almost half-hour to escape - I should have started charging a few quid each!
Regardless, Buckingham is one of those things that you can't miss, but don't expect to be bowled over. I never went to the changing of the guard - a friend who went said you end up in a cloud of tourists and can't really see that much of a pageantry that really isn't that exciting anyway.