These are the skills that don't easily fit into any other category. They aren't too difficult to develop, but they do take time and you really have to plan out how to develop them.
You improve this skill by jumping and falling. Each time you jump, you get 0.15 (base value) skill increase points. That means it will take a lot of jumping in place to increase your skill. You get 3.0 (base value) for falling. Whether this includes falls where you take damage or not, I don't know, but I assume not since it's based on successful use of the skill. Find yourself a low balcony (where failing won't kill you) and jump off of it for a while.
You develop this skill by repairing armor and weapons. Don't use Apprentice's equipment or repair prongs unless you absolutely cannot avoid it. The quality is so low that you actually suffer a penalty to your Armorer skill when you try to use them. Each successful repair (indicated by a "ding" rather than a "thunk") gets you 0.40 skill increase points. Most Smiths and such carry Armorer's Hammers. Since they are heavy (4 pounds each for Apprentice, 3 pounds each for Journeyman, 2 pounds each for Master, 1 pound each for Grandmaster) and only have 10 uses, you probably won't want to carry around more than one or two and you'll want to use them up as quickly as possible so that you have room in your inventory for the more valuable stuff.
For additional skill working, repair everything in your inventory before selling anything to a merchant. This accomplishes a couple of very nice things. First, it develops your Armorer skill. Second, it makes nice, neat little piles of equipment in your inventory so that it's easier to work with. If you have two iron cuirasses in your inventory, each in a different state of repair, it will show you two cuirasses. If you repair them before trying to sell them, it will give you one stack of two cuirasses. I haven't noticed that it has an effect on the final price of an item, but it might.
Running (0.02 points per second) and Swimming (0.03 points per second) are the two actions that develop this skill. Note that the skill increase points are based on the number of seconds that you do the skill. But the skill increase points are so low that it's hardly worth the bother. I usually run everywhere just because it's faster that way, but it's honestly easier to just pay a trainer.
You develop this skill by bartering (0.3 points) and bribery (1.0). Invest a few hundred gold in training if the skill is low, but once you're above about 30% skill level, it should take care of itself. Especially if you have a decent Personality attribute. Bumping up the price by 1 gold piece is enough. If you get "your offer is refused," toss in a cheap item and bump up the price by 1 gold piece again. A successful barter will increase the disposition of the merchant by 1 point. An unsuccessful barter will drop the disposition by a point. So, like they tell you in sales, the key is to "keep them saying yes". And don't say goodbye until you're finished. That disposition increase is only temporary and will disappear as soon as you terminate the dialogue.
You'll see faster skill increases by bartering for the maximum possible amount. This one is a little trickier, but not too difficult. You'll need a fairly large stack of items to sell and the willingness to spend a little time tinkering. Sell the first item and then bump up the price by a gold piece or two for each successive item. When you hit "your offer is refused," you've hit the ceiling for that item at your current skill level. Sell for the maximum amount for the maximum skill gain.
Bribery is a little easier, but a bit more expensive. I combine Bribery and Taunting when I need to get an NPC to initiate a fight. I Taunt them until their disposition is down near zero and then bribe them to get it back up, then Taunt them again ("now go away you silly ka-nig-it or I shall have to taunt you again"). The gold that I used for the bribe is in their inventory, so it's a no-lose situation unless I run out of gold before I have managed to force the attack. Keep in mind that it's easier to bribe someone with 1000 gold than it is to bribe them with 10. Some NPCs who will love you for 1000 gold (the disposition increase from bribery is fairly permanent, by the way) will hate you for a failed 10 gold piece bribe.
You can only increase this skill by training or by successful Admire/Intimidate/Taunt. It just so happens that Caius Cosades (whose disposition will rise to stratospheric levels before he disappears from the game) will train you in Speechcraft. And because he likes you so much, he will do it cheaper than almost anyone else. Take advantage of it. Each time you report back from one of his quests, blow a few hundred golds on Speechcraft training before taking off on the the next one.
As an aside, I have had a few Speechcraft skill increases after successfully bribing someone. I suspect that those were hiccups as the game is supposed to treat Bribery as a function of your Mercantile skill, but I've never really been one to turn down a skill increase, no matter where it came from.
Keep in mind that disposition changes from successful Intimidate is temporary. After you close the dialogue and check back with the NPC, you will find that they like you even less than they did before.