Right now I manage around 10 horizontal top bar hives and 12 Warre hives, so my methods may be a little different than someone with only a hive or two.
All of my top bar hives at this point have side entrances. Usually 2 toward one end, 2 centered and 2 toward the other end. I start colonies at one end and let them expand in one direction. I keep a follower board on each side, however, so I can easily access both sides of the colony.
I generally go out to my HTBHs every couple weeks and at minimum check for comb production and, as needed, expand the cavity (2 follower board hives). Monthly I go through most combs in the colonies, check for cross comb, and fix or remove problem combs. As you've probably seen, most cross comb begins once they start expanding combs for honey storage. Therefore, most issues are at the far end of the hive where the freshest combs are.
I don't use smoke in any of my HTBHs.
I start by looking through the window and checking for the location of the last comb. Next I move the follower board over as far as possible to give me ample space to shift combs out of the way after inspecting. If needed I'll remove all the spare bars from the hive and replace them once I'm closing it back up. As I move through combs and shift them out of the way, I make sure that I keep them flush with the other bars I've already inspected. This way, when putting the bars back, I can move 2-3 at a time and minimize the time it takes getting bees out of the way.
Honey combs will usually have attachment up at least one side of the comb. I quickly check both sides prior to moving it. If there's attachment I slide a hive tool down each side to remove the attachment, then I cut through the propolis holding gluing it to the next bar and shift it over.
Using this process I can generally get through 10-15 combs in 8-10 minutes, as long as there's little cross comb. This usually allows me to check honey stores, eggs and disease and get the hive back together.
The most difficult part of top bar hives is learning to work with the top bars themselves. Once one is comfortable removing and manipulating the bars -- especially the fragile, fresh honey combs, the process can go very quickly. Having worked in Langstroth hives, Warre hives and HTBHs, I can genuinely say that I MUCH prefer to work in horizontal top bar hives. I find myself killing fewer bees than the other two options, and I don't have to lift any heavy boxes.
Cheers,
Matt