I see someone above me has already offered most of the "cheats" (personnel and aircraft transfer bugs, etc), so I'll just offer some tips:
1. Don't build a second base too soon. As long as your base is in a decent area (the guide suggests somewhere like central USA to cover your biggest sponsor, I prefer building it somewhere like Switzerland to cover all the Europeans) you can get away with a single base provided you immediately build a large radar centre, which brings me to my next point.
2. Radars only have a 5% chance of detection every few minutes. This means you shouldn't dismantle your small radar just because you've built a large one.
3. If you attack a UFO with sectoids in it (they look like the "greys" from films/games/etc) try to capture some alive. They're a common early race and crucially, capturing the ship's navigator and interrogating him will let you build the hyperwave decoder - this building has a 100% chance of detection and will even tell you what mission/race/destination an alien craft has.
4. Your own aircraft carry radars (with much smaller range, of course). If you lose sight of an alien craft tell your interceptor to continue on the same bearing - occasionally you get contact back.
5. Check the graphs! A very useful one is the one that details UFO activity on a per-country basis. If there is a spike of activity in a certain country it could imply there is an alien base. To detect alien bases, get a skyranger (because they have lots of fuel) and tell it to patrol to a random spot in the country. After a little while (not very long, its not like you have to spend all of your fuel sat in the same spot or anything
) if there is a base nearby it will show up as a pink square on the map. Smash it for lots of points! When you get the hyperwave decoder and you detect supply ships on 'Alien Base' missions, it's time to send the skyranger near the ships destination to see if you can spot a base.
It is sometimes worth letting the base be. Supply ships will come down every week or two and if you can reliably shoot them down you can get a LOT of resources from a raid of supply ship crash sites. Do watch out though, after a while the alien race in question will start retaliation missions - they will try to find your base and mount a raid on it.
6. Aliens occasionally send infiltration missions. These are particularly annoying, and consist of three UFOs: two very large (battleships, do not try to shoot them down) and one large ship (I can't remember the type). The battleships will land in two cities in their target country. You must either shoot all three craft down or shoot the large one down and assault both battleships on the ground - good luck
7. If you lose sponsors, this isn't the end of the world. Most of your money will be made from selling all this alien loot you've been stockpiling, and making some of your own cool stuff to sell! Items which cost less to make than to sell (and which can be built relatively quickly) include the laser cannon (for aircraft) and the motion tracker, in descending order. If your engineers aren't busy, tell them to build as many cannons (or trackers if you can't get cannons) as they can and sell them off immediately.
Good alien items to sell include:
- Mind probe (you only really need one, and they sell for a lot of money)
- Alien corpses (you only need one, and then you don't need it when you've researched it)
- Plasma pistols/rifles: I much prefer the heavy plasma, which is almost as accurate, not particularly 'heavy' (even little sectoids can carry one!) and incredibly powerful, you will get a LOT of money selling off a dozen rifles and pistols after every other mission when you see aliens in bigger numbers
- Alien entertainment/other 'miscellaneous' research objects.
You want to research ASAP:
- Laser rifles, and then equip everybody with one. They're light, don't use many TUs, quite powerful and have infinite ammunition
- Small launchers/stun bombs (you need to capture some aliens, and this is the safest and fastest way to do it)
- Heavy plasma/Plasma cannon for soldiers/aircraft: with a plasma cannon on aircraft you have a higher range than every UFO except for the battleship. This means you can just set to 'standoff attack' when you intercept every single time and never take damage! Can also be done with avalanche rockets, but this won't work every time.
This game is huge, but I better stop before I end up writing a strategy guide in the thread