But I still find myself perplexed when I read people talking about that wrt the magical arts, to speechcraft and to mercantile because except for destruction IMO they are very easy to increase. It's more as if the issue for players is that they can't raise the skill as fast as they want rather than that they can't raise the skill. I'm probably in the minority because I now only use a trainer for sneaking, but OTOH I never choose sneak as a major/minor skill anyway, so I seldom try it and more rarely buy training in it.
At one time, I did think it was hard to raise magic skills, speechcraft and mercantile, but rethought my strategy and realized it is easy, all the time keeping within the rules and spirit of the game. One of the first pieces of advice given is, practice your skills. I blinded myself to the possibilities thinking I had to stick with the spells I started with or purchased. I knew that you could buy customized spells, but it wasn't until I had played a lot of games that it dawned on me, not to make spells to kill the enemy but to make spells that only cost 2 or 3 spell points and last just a few seconds. In many cases it's pretty cheap to make those type of short-term spells. The point isn't to try to use it against an enemy but to be able to cast it frequently enough at a minimal magicka cost because practice is the only way to improve the skill.
The mages advise to buy a variety of spells for customizing. Again, I had tunnel vision thinking 'bigger' and 'more powerful'. But if you step outside of that mindset, follow the game advice to buy a variety of cheap spells in each of the magicka categories and then customize one of each type. In my case, I choose spells that affect only me. I usually have a spell to practice: conjuration (e.g., binding spells), alteration (levitation, lock), illusion (night eye), mysticism (recall, intervention, soul trap, righteousness) and restoration (fortify). Destruction is the only school of magicka I haven't found a satisfactory spell to try. I cast these spells while on the move, they don't antagonize bystanders, and I use alchemy or sleep to restore my magicka.
Alchemy is very easy to raise, especially if you're willing to use yourself as a guinea pig. IIRC, the NPC who tells you to practice also gives you a hint about alchemy. Regardless, all you have to do is sample the various ingredients (animal, vegetable, mineral) you gather and make note of what the effect was so that you can decide whether to consume it in the future. In my case, I add notes to the game world map to remember. The more frequently you eat ingredients or later acquire and use alchemy equipment, the quicker you raise your skill. And you're given hints if not explicit info about specific ingredients that have useful effects. This is one skill all my chars work on developing ASAP. But it's so easy IMO that I don't select it as either a major or minor skill.
Enchanting seems relatively easy if you can keep yourself supplied with soul gems containing trapped souls. I get frustrated with my attempts to enchant an item because there is a high failure rate, but you can also recharge enchanted items. For whatever reason, I don't find that as frustrating. And each successful event increases your skill.
Once I reread the game info about speechcraft and mercantile, I've found that they are easy as long as you are patient. NPCs repeatedly advise you to spend your money to improve cooperation and that using spells or potions to increase your personality for the short term can backfire. You improve your speechcraft skill via persuasion which includes bribery and several non-monetary alternatives. My chars choose to use bribery, which works as long as you have the gold If the bribe fails, then I back off and return another time. Regardless, bribery is an effective way to improve your speechcraft and can be practiced more often than the alternative methods IMO.
WRT mercantile skill, there are two things going on when you barter. You can see that the merchant's disposition moves up or down each time you make an offer; up if accepted or down if rejected. Again, you get advised to deal with merchants who like you (disposition). Bribery can help here. But AFAIUI your mercantile skill increases when you successfully negotiate a price favorable to you relative to what the initial offer was from the merchant. So my strategy is to barter either on a 'high' priced item or on a sufficient quantity of an item and just go for a minimum change in my favor from the merchant's offer. My objective is not to get the "largest" monetary advantage in the sale but to make an offer the merchant would immediately accept but is still favorable to me, thereby increasing mercantile skill.
The one word I'd stress about raising skills is patience. Your char has to develop his/her skills over time. For me, that is part of the fun of game. With the exception of the sneak skill, my experience is that all the skills are very easy to increase. The only reason I single out sneak is because I don't have the patience for it Until I modded my game with MCP, sneak was not only tedious but physically uncomfortable. Now it's just tedious.
Hope you'all find this helpful.
John