+1 everything said already.
OP welcome to HOI! Since I'm not sure if you're playing a major or a minor country, allow me to streamline a little further.
If you're a major, yeah build tanks, and CAS, and win the air war, and SPART, and Rocket Art, and Space Marines (1 HTD in each Infantry unit) and 40 width everything. Then just right click on your enemy's capital and go make a sandwich, wait for the peace conference to proc.
If you're a minor country, or somewhere in between figure out what you're capable of with your country limitations. Do you have manpower? 40w is really good. If not use artillery everywhere (or both ideally). Put artillery in support companies, but also as battalions within your infantry division (this is called line artillery). The soft attack from artillery is fantastic for chewing up enemy lines. Rocket artillery is slightly better if/when you can research it (and build it).
Then once you have these, you can push fairly effectively with infantry using the battle planner to build up a planning bonus (attack bonus) and then, rather than clicking execute (which you can do but its a waste of manpower), find a few provinces that are either under-defended and/or can be attacked by multiple adjacent provinces at once. Use CTRL-RIght Click to order a unit to support attack in an adjacent province but not actually move into that province. Attacking from multiple directions gives a bonus to attack, and expands the combat width which allows more units to participate in the active combat. This should help burn down defenders even more quickly. If a defender from an adjacent province starts moving into the province that you're attacking (to reinforce the active battle), use an adjacent unit of yours to initiate combat on that unit BEFORE it can reinforce (even if you know you can't win). By pinning all potential reserves you stop them from reinforcing the battle you really care about.
Once you win, exploit quickly. Move into that gap, and try and hit the province behind the gap, not adjacent provinces that are still part of the old line (and thus have dug in units). The units that you just defeated will be disorganized with no entrenchment so attack them immediately because you have a big org advantage. Bounce them into the another, deeper province. Keep bouncing them, don't give them time to rest, reorganize and entrench. Smash them!
If you don't have a huge industry, cavalry is REALLY effective at exploiting gaps and running wild behind enemy lines. Make them.
At some point if you've made a truly deep push the AI will start to strategically redeploy to cover your push (you've broken the lines). This is where the fun starts, keep pushing but now start looking at old parts of the line. You should see gaps, under-defended provinces and provinces that have units with little to no organization. Start smashing those areas too using the tips above, and keep pushing (bouncing) them back.
Good luck, our addiction meeting is every Tuesday at the local YMCA
