Depends which side you're playing
Germans should use their early strength and Soviet panic by making even costly attacks and advances to make gains, but general rule should still be to preserve forces and attack with good odds. I like to do hasty attacks with multiple units since you can preserve MP and still get 10:1 odds.
CPP can however change my behavior, since all the participating attackers will lose 50% of their CPP. Thus a deliberate attack might be more resource efficient, depending on the units you have at hand. Units on the move with low CPP will get the most benefit out of hasty attacks, since they won't be losing CPP (that they never had in the first place). Make sure to have an unmoved HQ backing up your hasty attacks to get the support units involved!
For the flow of the game it's really difficult to give any general advice (ie should you attack after Jan 1943 etc). This game is HUGE, and there are so many variables that if you want the perfect answer, you need to consider all parameters. The attacking unit: strength, CPP, fatigue, experience, terrain/fortifications, weather, supply/fuel, MP, leader, support, ground support to list a few. Defending unit: approximations of strength, fatigue, supply, leader and support.
The map situation often dictates what kind of attacks you need to make. Sometimes you need to do unfavorable exchanges, and quite often just decline to attack, especially due to bad weather, terrain or other conditions.
Attacking is not the only option; maneuvering around the opposition can present gains in the form of pockets or massive forced changes in the enemy lines. Sometimes just a single unit crossing one river can force the opponent to reform their line completely (and pull the hairs out of their heads in real life).
WitE2 rules encourage attritional attacks in some respects, like reducing enemy CPP and MP, or causing losses in general. I'm not a fan of these when playing Germans, but I'm sure there's a place for these at some point of the campaign for the Axis side too. Soviet attritional attacks can be an efficient tactic if executed properly. Try to aim for at least 1:1 odds to reduce their CPP at least 25% if you suspect a strong division preparing for an attack.
All in all, experience matters if you're looking for a more grand strategic view of the Eastern Front operations. The more you play this kind of games, the more gut feeling you get what you should do and when. Early targets, potential advantageous avenues of advance, risks and rewards, expected weather, winter preparations, pocket opportunities, major ToE changes, army and command reforms, river lines, areas with exceptional terrain, !LOGISTICS!... you name it. There's a lot to learn, and that's one of the best part of these games!