Here are just a few early thoughts about the game after playing through about half of the scenarios and most of a campaign. I'm still a newbie to this, but here are some things I'm finding (experts may disagree with these, and I'm interested to hear what others have to say).
1. Some have commented on the small maps in general. This (and the general setup of units on the maps) generally creates a high density of units - two long solid lines facing off against each other across a large part of the map. The trick then is to find viable weak spot/s in the enemy line. Thus, the key to any given scenario is to first find that weak spot (or more) and organise a plan to exploit it whilst extending your supply line towards the victory objectives.
2. I emboldened viable, because ultimately you need to pursue an advance along a supply-able path. Thus, the first thing to do when opening a new scenario is to work out what supply sources AND supply routes (emboldened for emphasis) will allow your units to reach the enemy objectives. Count out how far each supply source can reach. Many sources simply will never allow your units to reach the objectives (so, generally, don't pursue your main line of advance from that source [caveat - unless you plan to link up with your main supply source in the turn or two thereafter]). Instead, follow the railway lines and see how they can support your advance. The AI will make an effort to defend these lines, and you can't simply by-pass them. You need to clear the lines (and those pesky one or two AI defenders) to clear your supply paths.
3. Zones of control are easily negated by the AI, so you generally can't really use your own ZOCs to your advantage. You generally need to have a solid line of units (with no spaces) blocking key 'open' routes (ie: routs to your supply paths with no river barriers). Unlike other wargames, the AI will not just fall back and form a new line, they will advance (suicidally) and attempt to cut off your supply at any opportunity.
4. The AI is generally hesitant to do river-crossings. They'll exploit any available bridge crossing, but will rarely cross a river (costs entire movement to do so). You can use this to your advantage by (generally) minimally defending the opposite banks of rivers.
5. The AI will exploit gaps in your lines, and thus they look for offensive opportunities (even when in defensive positions) to poke a hole in your line and advance through it. Thus, even when advancing, you can't give the AI any opportunities to poke a hole in your line that will threaten your supply. Keep a particularly watchful eye on AI cavalry (I found these easy to miss at first), mechanised and armour units (they all move fast). Don't have a 1 step unit defending a vital railway supply path (or a part of the line near a vital supply path). The AI will destroy that unit, then flood through it, cutting off all units 'down-supply' from that point (and they don't care if they die in the process of doing so).
A lot of 'generalisations' there, because there are exceptions to every rule and situation.