It's a pretty fun game, but it has a lot of luck involved. It's for 2 players (though possibly with 2-player teams), very quick to set up and learn, plays relatively fast (unless your opponent has OCD), and has both quick 2-hour scenarios and a full campaign game that can take maybe 12 hours.
There are 10 turns, each one with 5 impulses, each one representing one year. Within an impulse you do the usual move and attack. The only difference between the first impulse and the other four is that you can move and attack all you want in the first impulse for free. The other four impulses you have to expend a supply point (costs 1$-2$) to move and/or attack with a stack of units.
The start of the turn has random events and collection of money. Simply put you get 1$ for every city you physically occupy, an extra 1$ if it's on a trade route, and double if you have built a Colony or Trading Post there. Some special places (e.g. Orenburg, Delhi) or provinces (e.g. North India) also give you extra money.
You can use that money to buy supply points, civilization counters (e.g. colonies, trading posts, forts, and railways later on), leaders, and combat units. Reinforcements are placed in that country's home cities, or for the Russians and British, either their off-map boxes or else colonies they have built on the map.
Leaders can be used to help you in combat, but you can also send them into neutral or hostile countries to try to negotiate for control (or defend against your opponent's negotiation).
Each impulse is the usual "move, negotiate and attack." Movement is pretty speedy along roads, but agonizingly slow anywhere else (like mountains). You also get irregular units which have extra movement points and can also move diagonally. These are weak units, but they're doubled in certain terrain.
Of course the fastest way to move is by lake and/or river. You can actually move the entire length of a river and/or sea at no movement cost, provided you aren't going through mountain or enemy units. It costs you an extra 2 supply points, however (only 1 extra if you start in a port). There will be battles over control of the rivers and lakes!
Negotiation is fairly simple. You add up the political value of the leader you have in the country's capital, subtract the VP value of the country, and make a few other modifications, then roll on a chart. This is where the luck comes in. If you're good at rolling 6 you'll quickly find have the map allied to you, and you'll do quite well.
Why ally a country? You can move through neutral countries provided you don't end a move within their borders, but actually controlling a country lets you end a turn in one of their strategically located cities. You also get a lot more money for any cities you occupy in these countries, and of course you get to move and attack with their units. In fact, their units can be quite handy: they're rebuilt on the front lines instead of in the off-map box your units are built in, plus they can attack your enemy's units without triggering "open war." (Open War costs victory points and gives your enemy instant cash).
Combat is fairly standard. If your units end a turn in the same space as enemy units (or neutral units that have just now become enemy units), you fight a combat. You create standard combat ratios and roll on one of two charts depending on the types of units you have. Basically it's either a regular attack or more of a raid. The game also has a fog of war where you can't examine an enemy stack, so you never necessarily know what your odds are until you attack. Cities double the defenders, and forts triple, so you could easily get wiped out if you attack the wrong stack.
After the combat you move the balance of power depending on the units lost. Balance of power leads to victory late in the game, and having an edge in balance of power can help negotiate for minor countries, and also gives both sides more money each turn.
After the 5 impulses are over, you have to supply your units. In many cases you can forage. For instance, 6 steps worth of combat units can survive in a city (7 if it has a river). If you're "overstacked" then you have to pay a supply point to keep them alive (or else take them off the map). Also, stacks of units that are outside their own country (always the case for Russians and British outside their off-map box) have to pay another supply point over and above, so don't get too adventurous dragging your minor country units all over the map!
The balance of power display is the modified for various events, and then you're ready to go onto the next turn.
The game moves pretty quickly, and gives you a real feel for the period. Very early you learn the very strategic points of the map: the ports, cities along rivers, cities along major routes (e.g. near Bokhara) or near passes, etc. The game is largely a struggle to control those locations.
Here's a general flow of the impulses:
1st impulse: You move all your units into giant stacks in strategic, central locations. You generally leave single units garrisoning all the cities (for money collection), unless they're threatened by the enemy. Those you leave empty for now, and promise yourself to occupy in a later impulse. You take a look at what important countries are neutral, and send your leaders in there (by themselves: if they fail, you don't want to trigger invasion by having combat units tagging along!). If your enemy has left some single garrison units unprotected, you go stomp on them and improve the balance of power in your favour. If your enemy had left a key point undefended last turn in order to not have to spend supply points on it, then it might be a chance for a big attack. Even then you won't do better than 2-1 because he's probably in a city (or a fort), which doubles (or triples) his defenses.
2nd impulse: In regions where you're in parity, you have a stare-down where nobody moves until the late impulses, except in reaction to an enemy's move. It's a lot like chess between even players. In regions where you're dominant, you use these impulses to stomp on his garrisons and clean out any enemy units or civilization markers.
3rd impulse: Same as 2nd impulse.
4th impulse: Now you've got a better idea of how many supply points you'll need for supply at the end of the turn, and therefore how many you can use for operations. If you have enough, you might go try a few more negotiations with minor countries. You might also get an opportunity for an attack, knowing that you still have an impulse to capitalise on success, or else re-group or try again if you don't succeed.
5th impulse: This is where you spread out so that you're within the foraging values and therefore don't have to expend supply points. You also scramble minor country units back to their own country to save on supply points. You also spread out any garrisons, if it's safe to do so. This might cost a lot of supply points, however, so maybe you don't. But sometimes with a single supply point you can walk a stack somewhere dropping units off on your way. Of course, dropping off slower units does NOT allow the faster units to go any further, and you can't pick up units as you go.
Early Game Tips:
If you're Britain, you need to secure Afghanistan. Every avenue of attack into North India (your heartland) goes through Afghanistan. Furthermore there are a lot of critical routes that go through northern Afghanistan. Once Afghanistan is secure, you want to align all the minor countries back in your area, especially Sind and Punjab. They're easy to align if you have North India, easy to defend, and produce more revenue than other minor countries. Unlike the Russians, you really don't need any minor countries outside this area in order to keep the money flowing in. Offensively, control of Afghanistan gives you options to lash out towards the major river routes (which lead to the heart of the Russians), and you can also threaten Persia by sea. Persia is vulnerable - it's hard for the Russian's to reinforce because the mountains prevent reinforcement by sea, and the only other way is either through long, roadless, neutral Turkmenistan, or else all the way through the central part of the map.
If you're Russia, you want to try to secure the northern neutral minor countries as soon as possible, especially Bukhara, Khokand and Khiva. Control of the river and lake routes are critical. Once you're established in Bukhara, you're in a great position to counter any British moves, and if you're strong enough, to march through Afghanistan and into India. As for Persia, I would just built a fort and fortify it. If the British want to take it they'll have to commit everything, probably leaving them too weak to defend Afghanistan (which is far more critical). Once you're established, swing a leader up to Sinkiang if you can. It's a relatively easy to defend way of earning extra cash every turn.