When one player has more artillery than the other, the player without the artillery is probably going to be forced to attack. They can endure the attacks hoping to draw some artillery cards as the game progresses, but this is hardly something that can be counted upon, especially if the opponent is hitting them with five or more CV's per turn. They are likely to take at least one hit every turn, sometimes more. In this situation, the player without the artillery is forced to attack.
Given that an attack must occur, there are two ways to pull it off. One is to mass a group of attackers in a position and march them all forward at once. This will work but there is a much more elegant method.
A better approach is to march one number less than the maximum allowed forward to the attacked position. Before you do this, take a long range shot at the position with the best artillery that you have available. Hopefully you will hit at least one of the cards. Secondly, engage a flanking attack with two infantry cards, supported by a general. If only one of the flankers fails to flank, you have lost nothing and the general stays in the position. If they both flank, one is routed due to stacking limits, but you still get that immediate attack from flanking card that succeeds. Lastly, if the position is defended by a general, use the sharpshooter card to shoot him. Place a couple cards in the corresponding position so that you can replenish the attack in subsequent turns.
If you don't have the cards in your reserve necessary to attack in this fashion, you probably shouldn't be attacking unless you are in one of the aforementioned desperate situations. You should plan on losing at least 50% of your units in an attack against a moderately sized force, and you'll need cards in your reserve to replenish these losses. Of course, when it's late in the game and both of you only have seven or eight combatants, this suggestion is moot.
Another consideration is to attack two or three positions at once. This limits your opponent's ability to pull reserves from the front lines to defend a weakened position. It also forces him to expend reserves to two or more positions, instead of allowing him to concentrate all of his relief effort to one position.
ATTACKING ARTILLERY
One thing to remember when attacking artillery is that artillery are really lousy in a melee situation. If you can get a good bunch of infantry and cavalry up against a large artillery force and survive the initial assault, call a melee in the attack phase. Your forces will hit on 4-6 while they only hit on 6. That's an incredible advantage. This is why I NEVER create a position which consists entirely of artillery. It's just too vulnerable.
Another thing to remember is that artillery cannot fire over the heads of cards that have engaged them. Sometimes I will use a 1 infantry or cavalry as a screen while I assemble an attacking force. The opponent usually kills this poor unit, but more importantly, the units behind it are spared. This also requires your opponent to show all the cards in that position, which can alert you to any potential problems that may affect your decision to attack. One key to remember in this situation is that artillery must attack this "screen" card individually. Thus, one artillery shoots, then another, then another. The unit is immediately eliminated when it takes MORE than its CV in hits.
A good counter to this strategy is to march a "disposable" 1 infantry or 1 cavalry forward and engage a position that you feel may be gearing up for an attack, especially on a vulnerable artillery position. It will immobilize these potential attackers and prevent from advancing on your position. This will give you one or more turns to reinforce this positions or re-allocate the cards at your disposal. If by some chance the unit lives, shoot anyway (unless you are planning to move the artillery somewhere else) and be sure it fires BEFORE the artillery, because it will suffer "friendly fire" hits on artillery rolls of 1.
General Strategies
When to Attack and How (this page)
Other Strategies
Breakdown of "Special" Cards
Strategies for Each Side