Heroes /sov learn new spells by leveling up, and choosing the spells from the schools (earth, air, fire, yada) they know.  New schools may be added via special events / quests/ and most easily, via books.  One faction (P..yada)  unlocks all the books at a certain tech. If P.. is in your game, make nice and go buy the books.

Better units?  Level up (^ population) your main troop training citadel.  Did you make your main citadel on a space with several mana resources?  -so you can enchant the citadel with spells that add magic to troops trained there?  Can you do any more quests?  One faction gets to buy quest starting books.  If in your game, make nice and go buy some. 

Beyond this, I am at a loss to suggest anything else.

You can do a couple things. Go into unit designer and make some better units. Keep researching the warfare path and get better weapons and upgrade the units you already have. Research to gain bigger armies (these are spread out in both warfare and the civilization trees), or research something like logistics (in civ tree) to gain bigger squads (i.e. going from 3 units per trained unit to 4 units per)

Exactly, you are looking for the techs that say +1 Army Size. For instance, look at "Drills" research in the warfare tree, when you hover over the little up pointing arrow icon you'll see it says +1 Army Size, then just look for others in the tree with that same icon.

As others have said, make sure that your world resources have been built upon (iron deposits for metal to allow advanced armor and weapons, wild horses and wild wargs for mounted units, crystal crags for enchanted weapons and armor), because otherwise you don't have the resources for certain types of troops. Note that even if you have done so, you may still need to wait a little while to allow your stockpile of resources to accumulate enough so that you can train a unit using those resources (mounted units require one mount per figure in the unit, of the appropriate mount type - horses for horsemen and wargs for warg riders).

The Warfare and Civilization trees have techs that allow you to increase the size of your army; Leo named one of them. The Civilization tree also has techs that allow you to increase the size of your units, which allows you to increase the power of your armies without increasing the number of units in them - look for techs like Cooperation for this.

Other things which you can do to increase the power of your army:

1. Switch to magic weapons of a similar tech level to the mundane weapons you're currently using - magic weapons are often very nearly strictly superior to mundane weapons, assuming you can afford the crystal costs.
2. If you're looking for a basic ranged option, use the basic magic staves, not the basic bows. Magic damage bypasses armor, and most factions can have at most 50% resistance to either Fire or Cold damage, but not both; moreover, no non-Altar unit can have both positive Fire and positive Cold resistance. Beyond that, magic staves have less of an initiative penalty than the basic bows and are only slightly behind the advanced bows. They also require less research, though you need to have a crystal supply in order to train units using these.
3. Make use of the city buff spells which benefit trained units (Heart of Fire, Aura of Might, Aura of Grace, Aura of Vitality) on a high-essence fortress and train most of your army there. These will provide +1 Fire damage/defense/initiative/health per essence to each figure in the unit (defense and initiative are not cumulative over the figure, but damage and health are; thus a 3-essence fortress with Heart of Fire, Aura of Might, and Aura of Vitality training 3-man basic club troops will provide you with troops with 9 extra health, 3x3 extra Fire Attack, and 3 extra defense compared to the same fortress without those three enchantments; also, don't underestimate the power of Aura of Grace - +1 initiative per essence might not seem like much, but it's enough to allow your troops to go first and potentially gain extra turns when fighting equivalent troops trained by an AI faction at some random city).
4. Make use of whatever curses, blessings, and damage spells you can - even without Death Shards, Wither will reduce enemy damage output by a reasonable amount; Haste and Slow can significantly affect the outcome of close battles, as can either of the healing spells; Giant Form, Diamond Skin, and Growth are good boosts for front-line troops; Shrink and Blind can occasionally allow you to ignore certain enemy units; Fireballs and Blizzards can kill armies (you can get Blizzard Scrolls from Level 3 Conclaves if you take the Scroll Scribe option when the city advances to the third level if you don't have a champion with Water IV, but they cost a fair amount of gold to purchase).
5. Use more troops than champions in your armies - I prefer to have one or maybe two champions in each of my armies for magical support and traits that benefit the army, but no more than that when fighting the AI. This is mostly since low level troops with decent equipment are usually superior to low- or mid-level champions, especially if those champions lack decent equipment. If you prefer armies of champions, you can make that work too.

If none of the other advice in this thread helps out, I think you can also destroy the city using the spell Curgen's Volcano, which I believe takes 2000 mana to cast and can be found in the Magic tree. This will wipe out the city and its defenders, so you won't need to worry about creating an army capable of conquering the city. I have never used this spell, though, so I don't know how well it will work, or if it can be cast within an enemy faction's borders.

To upgrade units which have already been trained, there is an 'Upgrade' button under the main screen unit overview (the selection panel in the bottom left corner of the screen). It may be hidden in the '>>>' menu on that panel. Upgrading units will cost you gold and resources for equipment upgrades, and gold for unit size upgrades.

Be advised that, as far as I know, you can't choose what you upgrade to, meaning that you'll upgrade to whatever the computer believes is the best equipment for your units (weapons go for highest combined attack in the same weapon category - swords to swords/axes to axes/clubs to clubs/spears to spears/bows to bows, not spears to clubs or something like that, while armor goes for highest defense rating; no other bonuses are considered, so if you made a dodge-based unit which really needs the dodge from the Monk's Robe and the initiative from the Soldier's Boots, don't upgrade your armor). I also don't believe that there is a way to tell a unit to only upgrade certain items (your options are armor, weapons, shields, and unit size, but I don't think that design choices in the Unit Design screen affect this - i.e., if you tell a unit to always use Altarian Leather armor and 'best available' boots, when you order that unit to upgrade its armor you'll lose the Altarian Leather if you have chain or plate available, rather than keeping the Altarian Leather and changing the boots - but I'm not certain, as I don't usually care what my units are using as long as I can keep them alive and fighting).

Correct, it is unnecessary to build roads from resources to cities in order to make use of the resource. Be advised that resource structures are placed in the build queue of the closest city under your control (if you order construction of a resource improvement, and then found a new city which is closer than the old city was, the construction order will shift to the new city), and the basic ones usually take 3-5 turns to complete on normal pacing. This means that if you aren't paying attention to which cities your resources will be assigned to, you can significantly delay city development, and it can take a very long time for a new or high-unrest city to complete large numbers of resource improvements. Unfortunately, the only way to control resource construction assignment cities is to chose when and where you build your cities (potentially also razing some cities if you really, really don't want the resource to be improved by that location).

I do, however, tend to like having roads that at least come close to the resource, as it makes defending the area against raiders much easier, unless the resource is in a secure area. Automatically generated roads going between cities or headed off to nearby outposts are usually sufficient for this, though sometimes I like to make my own additions to the automatically generated roads.

Thanks again guys, beat my first game with Warlord Verga and 7 Juggernauts in his army. Was actually a piece of cake as soon as the first Juggernauts joined my army.