Totally late on this post! Sorry about that.
With two different types of comb, we used two different extraction methods to get the honey. For the two frames pulled from the Langstroth hive, we used a two frame drum extractor. This holds the frames and you spin them to force the honey out. The natural comb from the top-bar hive will not work in this type of extractor, so it has to be crushed to release the honey.
For the Langstroth frames, the first step is decapping. This removes or breaks the wax cap the bees place over each honey cell. If the cap is in place when extracting, the honey cannot come out!
I think most people use a decapping knife for this, but the inexpensive starter kit I purchased came with a tool that looks a lot like a many tined fork that you rake over the cells to cut through the cappings. It worked pretty well, so we will likely continue using it.
We caught the cappings and any honey that drizzled out in a cookie sheet. I've seen a number of better ways to do this online, but had not had the time to try to build something. I think that is something I will do next year, as this was a bit messy.
Once the cappings were removed, the frames went into the extractor. Our extractor fits two frames. It has a handle that you crank which, in turn, spins the frames around. You start out slow on one side, flip the frames over, and go slow again. You can then flip the frames over and go fast. Going slow at first helps prevent damage if you wish to reuse the comb in the hive.
As you spin the extractor around, the force flings the honey onto the sides of the extractor where it slowly finds its way to the bottom. It's pretty good exercise!
It takes a while, but eventually everything finds its way down. There will be bits of wax and maybe some pollen in the raw honey, but these will be filtered out. That cheap-o kit I purchased came with a pretty decent strainer to get the bigger things out. It is actually two strainers that connect to one another, a larger mesh first to get out really big things, and then a finer mesh below to get smaller items.
For the most part, that's it to extracting from the Langstroth frames. The comb from the top-bar hive is completely built by the bees. It can be an odd shape or size and it doesn't have the rigid frame around it, so you can not use the extractor to get at the honey. Instead you crush or chop it up to release honey.
We used nothing more than a potato masher in this process. No special tools needed here.
We then moved the results into the strainer. As the honey filtered through we stirred up the wax from time to time to let any honey trapped on top get through. This process definitely took longer than the spinning extractor, but since you are cutting up the entire comb, you do get to reclaim more wax. The general rule that I've read both in books and online is that you get more honey from a Langstroth hive, since the bees spend less time building comb on premade foundations, but you get more wax from a top-bar hive. So far, this first year has certainly borne that out.
In the end, from the three frames, we extracted a bit over a gallon of honey. Not sure if that is normal or not, and frankly, don't really care. I think it is awesome that we were able to get any in the first place.
Once all of the honey was in the bucket, we did a final filter by passing the honey through a cheesecloth. Because this process can introduce a lot of air bubbles into the honey, we let it sit overnight before doing anything else. This also gives anything that made it through the filters time to either float to the top, where it can be skimmed off, or sink to the bottom where you can avoid it while bottling.
When we checked back the next day, there was very little to skim off. Between the mesh filters and cheesecloth we seemed to have removed anything that might be a problem (there's always some pollen in honey - it's good for you!)
We got thirteen jars of beautiful golden honey. It has an amazing flavor. Can't make any claims on where the nectar came from, it is truly a mix of whatever has been blooming. All I can say is, it beats store bought soundly!