Be sure you're not making the same mistake I did when I first got the game and enabling ALL the other nations at normal difficulty.
I suggest, at setup, only enable 2 other nations (to start as a beginner), and put them on "easy AI" (which is a very misleading term for a beginner...they are NOT that easy when you're just learning the game). You say that after a few turns another nation already has nearby provinces, so it sounds like you're making too many nations active.
Resist the temptation to "buy the best". Recruit the cheapest units (about 20-30) and put them in the front-center of the army. Put your archers to the front but way off to the side (bottom and/or top as you look at the green box). Put your heavy-hitters off to the side a bit, slightly behind and to the side of your "cannon fodder" troops. Make sure you order all your Commanders, priests, and spellcasters to "stay behind troops". With this strategy, the cheap units will absorb the initial shock of the attack, and so what if a handful get killed...they're cheap. This will allow your other, more expensive units to break the morale of the enemy once they start attacking.
Income problems: When you conquer a province, there will be a certain amount of unrest (because of the war turmoil factor). First turn, lower the taxes to about 10% for every 5 unrest. ie: If unrest is 11, lower taxes to 70% for one turn. On the next turn, unrest should be zero (unless there's a hidden magic site causing unrest), so change the tax back to 100% on this turn. Always conquer the provinces that border up against your starting province first, as this provides your starting province with more resources for recruiting units.
With the cheap units, some will probably rout every battle and run to a nearby province, so have a "cheap commander" on hand that can round them up and bring them back to the front lines.
Don't use your pretender in melee if he's getting killed. Give yourself some time to learn the game mechanics. If all this doesn't help, no worries.
Do this:
When you create a new game, the Last screen you see has a bunch of options. The top one is "Strength of Independents". You can change this to a lower number, and it'll be easier to conquer provinces. Change "world richness" to a higher number to get more money. Change "special site frequency" (or whatever it says) to 50 instead of 40. I forget off-hand what the rest are, but they should help you be able to play a decent game. Just be aware that if you lower the strength of independents, it also makes it easier for the computer AI to expand.
Oh, and use the "Aran" (topmost) map to start.