Why train your squad members? Watch a group of sand ninjas carve their way through a hapless mob of hungry bandits and you've got your answer. Specializing your characters is a great way to make them more effective at their chosen jobs, as well as enhance their survivability when they do get into combat.
The following are a few things I've learned while playing entirely too much Kenshi. Note, this is just based on my experiences, so it's hardly exhaustive.
First, a point about healing. While it is reasonably straightforward to train specialized medics, there is a good argument to be made for spreading out medical training (and first aid kits) to everyone in the squad because having lots of people healing simultaneously is generally faster than one specialist running around healing everybody.
If you do decide to specialize one or two characters, liberal use of the "medic" button with your chosen medic (and only your chosen medic) is a great start, but you can take this much further by training specialized healers.
- Specialize! - Use only one member of your team to heal everyone until their skill reaches 40 or so. After that, it probably makes more sense to spread the healing xp around the rest of your group, because field medic stat gain is much slower after that.
- Craft - Get a medical crafting table (basic medical assembly desk or higher). Medical crafting increases Field Medic skill. Because as of .6x or so, characters still accumulate the associated skill when using a device whether anything is actually getting made or not, it makes a lot of sense to keep your medic assigned to crafting even if you're not actually making first aid kits.
- Heal your enemies - When you finish laying waste to your foes and looting them, take advantage of all that free healing xp by healing them up. Don't worry, with the way damage works in Kenshi it's very unlikely they'll be able to get back up and attack you. And if they do, hey they're only likely to get up one at a time and they're already beat up. More practice for your fighter types! As a possible side benefit (depending on your goals long term) you'll also earn positive reputation with that faction, possibly reducing the likelihood of a future attack. This is also true of any non-hostile faction patrols you encounter.
Training engineers is pretty straightforward (at least, as of the current build). When building objects, simply have all the individuals you want to gain engineering skill work on them. They'll all gain experience quite quickly. You can also semi-automate this process by shift-right-clicking on a build project with all your engineers selected before you assign any other permanent jobs. Then they'll drop whatever they're doing and rush over whenever an engineering project becomes available.
Also very straightforward. Just give them a labor job and leave them alone. Supposedly strength improves labor performance, so loading a backpack up with heavy stuff and making them carry it around in their inventory (not on their back) might be helpful in the long run. I haven't noticed much of a difference in labor effectiveness due to strength, but I'll admit I haven't tested it extensively.
You gain experience by fighting, of course, but there are a number of things that can help make this process (literally and figuratively) less painful for your troops.
- Use light armor - Early on (until you build up your melee attack and defend skills) it makes sense to keep your fighters light - nothing but light armor or less, and focus on items that improve skills (bandannas, martial arts handwraps, ninja or assassin rags, etc). This is both because a -1 skill or +1 skill effect means a lot more when your base skill is 1 than when it's 50. This has a second benefit: it makes them faster and better able to kite enemies (see below).
- Fly a kite! - Kite mobs of slower enemies to build up melee attack. Training dummies are useful (sort of) but slow. If you don't mind a bit of micromanagement, you can speed this up quite a bit. With one or two light fighters selected, attack a bunch of mobs (it'll probably work better if you use "attack target" from the right click menu on the nearest enemy). When your character(s) squares off against the enemy, watch carefully and use pause repeatedly to determine whether your character or one of your enemies is going to swing first. If it's your character, great. If not, run away just out of range and then reengage. Rinse, repeat. This will keep enemies from surrounding you and can often allow you to kill large groups of enemies without a scratch. Of course, if you make a mistake, you'll probably get mobbed and bludgeoned into the sand. But that's good for your toughness skill, right?
- Take prisoners - Once you can build prisoner cages, you can build training rooms that will help you level up fighters very quickly. Build 4 or 5 cages in a house, and fill them with level appropriate enemies captured on the battlefield. Don't forget to heal them before you bring them home, though, so they don't bleed out on the way! Once an enemy has recovered (enough), send one fighter into the building, close and *lock* the door behind them, and then let the enemy out. Fight them until one or the other of you falls. If the enemy wins, unlock the door and send in the rest of your troops to flatten them. Then heal your trainee and the foe and return your training "partner" to their cage to rest up (you can also use a bed for this, if you're willing to micromanage recovery times). This works much better if you give your enemies weaker weapons (for instance, the terrible clubs you loot from hungry bandits). Early on, this can result in a point of melee attack or defense and a point or two of skill in your chosen weapon every time you win (or a point or two of toughness when you lose).
- Pump that iron - When not training or fighting, overload your fighters and assign them jobs where they'll do a lot of running. Alternatively overload them and assign them to follow a patrol or other traveling NPC around. A carried (not worn) backpack full of stacks of ore (or alternatively, heavy weapon clubs) makes a great set of training weights.