I have a ton of tiles (2x of each set, 5x times that in home made tiles), 20+ battlemaps (Paizo flipmaps and similar homemade oness), cardstock and wargaming terrain (20+ bins), and a slew of minis (7,000+ DDM) - so organization and usage has become very important to me over the last few years.

And to top it off, we often don't play at my house, so I have to port what I need to a second location.
So, usually before the game session I figure out what I'm definitely going to need terrain, minis and tile-wise, and also what I
might need, and then cart them downstairs or pack them up for travel.
As someone else mentioned, I'll lay out any tiles beforehand (usually the day of or evening before), and either take a digital pic, or quickly sketch out what I've done on paper. (Also previously mentioned is that the tiles are usually good approximations of the dungeons, but rarely exact matches. Don't sweat a few extra squares here and there. Its seriously no biggie.) I'll usually throw each dungeon level or encounter area into a separate ziplock baggie (the big freezer kind), so its easier to get them out during play. I try to place on an as-seen basis.
For minis, I do essentially the same thing. Figure out what I need, then bag them for ease of access. My minis are in plastic
Akro Mils large storage cases, and divided by type (I have some 70+ cases, plus a few larger containers I use for extra larges and huges), so sometimes if I know I'm going to have a ton of a creature, I'll just bring the whole case instead of bagging half the contents.
For the "might" stuff, I'm a little less rigorous, and just grab an extra case of tiles, bag some extra minis, and hope I get it right. I used to carry a pair of Chessex mats with me, and I may start doing that again as well.
FWIW, I do about the same thing with terrain and battemaps and such. Layout what I need beforehand, and then put it into a temporary storage for transport. I use
Container Store Underbed boxes to hold larger terrain in, and I keep an empty spare or two for transport.
For our initial session of Savage Rise of the Runelords (Paizo's Pathfinder AP), we had to take the SUV to my friends house; I had three containers of terrain, multiple minis cases, multiple smaller containers of misc terrain (fires, wagons, a well, etc) - and ended up creating a full 3D festival area in Sandpoint. It was pretty grand, almost 4' x 5' of playing area - a village square, complete with temple, tons of buildings, some 100 villagers, and a ton of goblins running around making fire.