Excellent suggestion from JimK, Matt; it would pay to heed it.
Okay...here's the basic steps:
1) Remove both crank arms using your crank puller.
2) Using the BB cartridge socket, start on the left side and remove the left cup/retaining ring, following these directions to remove the BB cartridge:
http://www.parktool.com/blog/repair-help/cartridge-bearing-type-bottom-bracket-service-bbt3) Loosen (or remove, if you wish to regrease them) both EBB retaining bolts.
4) Remove the EBB insert from the bike's BB shell.
That'll get everything clear to where you can clean it up and regrease/re-antiseize, ready for reassembly. Reassembly is the reverse of the above steps: Insert new EBB, secure with bolts, insert BB cartridge and torque tight to specs, mount crank arms and tighten to specs, replace chain, tension chain.
An additional suggestion in preparation for your long tour: Chains stretch on long tours, and sometimes they eventually stretch so much you can't take up the slack anymore by adjusting the eccentric. Instead, you have to remove a link pair and shorten the chain, then start over with the eccentric adjustment. Typically, the need for this task will make itself known during pounding rain and a headwind while climbing a steep hill in exposed country with no cover. It is then you'll be glad you took advance care to prep your chain with *two* quick-links on either side of an inner link so you can simply remove the spare section of chain and connector and -- voila! -- it is now short enough to once again snug things up leaving the proper slack using the eccentric. Sure saves a lot of time and aggravation when it really counts.
I learned this the hard way, deep in the middle of very rural Romania.
I shortened the chain and the factory mushroomed pin promptly dropped into deep grass. No problem, I had a quick-link. Big problem, the link was for 9-sp and Andy's bike turned out to have an 8-sp chain. All my spare quick-links were for 9-sp as were the ones he kindly provided as additional spares. 0.1mm can make a big difference at such times, as the quick-link just won't close without persuasion greater than a thumb and finger.
I owe the continuance of my tour (and avoidance of what would have been a 190km round trip bus ride plus lengthy hike to the nearest bike shop in C?l?ra?i) to a very kindly farmer who had access to a pair of pliers that allowed the connector to compress and then slide. To thank him for 150 minutes of his time, I went to the village store and bought him five of their best imported chocolate bars. When we met by accident a second time on my return trip, he greeted me with kisses on each cheek and forehead, a hug and hearty handshakes and called me Brother. He thought he'd never see me again after we parted the first time and had been very concerned about my safety and welfare. Those events make for some wonderfully Adventurous tour memories, but can be stressful at the time. Save yourself some hassle and take a
variety of quick-links, just in case you need to buy a replacement chain along the way. Not all chains come with quick-link connectors and those can save the day
if they're the right width. Be sure to save any chain links that need to be removed for sizing. They're "gold" if needed later for repairs. And be sure to properly thank anyone who helps you along the way and afterwards.
Best,
Dan.