Tips and strategies for the early game

The most important hint first:
Read the descriptions in the game - both research and UFOs, and also other stuff. These texts contain a good part of the storyline and the background, and also contain hints what you should do.
If you follow those hints, you shouldn't have too much trouble reaching your goals.

You can get additional hints from the gameset, if you look for the equipment you have. Weitere Hinweise zum Vorgehen kann man sich aus dem Spielsatz holen, indem man sich anschaut was man dort an Ausrüstung hat.

You start with 7 fighters, and building new ones only takes 3 days. The severely stronger bombers will take 4 days. On the opposite there are some 2 UFOs per day - so in principle you should have more fighters than UFOs can approach during production time. Should be pretty obvious that you will have to calculate heavy losses...

With the first small UFOs there should be a probability of 50% that you can crash them with a single fighter, but with the bigger ones, this won't work any more. Some players have posted, that they tend to save the game before attacking an UFO, to prevent losing their fighters, but at some point in the game even a Bomber won't have enough firepower to crash an UFO before running dry on ammo.

Therefore you will have to change your tactics sooner or later. By sending 2 (or more) aircraft, the first one will weaken the UFO, so that the second one can bring it down.

Don't forget to look at the different weapon systems you have at you disposal - the rocketlauncher is much stronger, but also slower, so that the aircraft must survive longer to launch all missiles. The gatling canon does less damage but has a high firing rate. Therefore the gatling is best used for the suicide fighter(s) of the first wave.

The other planes are an unarmed radarplane and 2 transporters. The radarplane, of course, is for recon the far side of earth - unseen scouts can get very problematic if you ignore them, and you have no possibility to build radarposts there in the beginning - the building times are far to long.

The transporters on the other side are for bringing your marines to the crash sides - you will need those artifacts.

In the end also some minor hints:

There is no difference in building time if you start an plane at 00:01 or at 23:59. So you should start building you planes shrotly before the end of the day, and then decide how many bombers and fighters you want to have. If you had heavy losses on the first day, you will need some more fighters to close the gap between day 3-4, but if you had minor losses you should completely change to bombers.
You don't need to down every UFO. Of course if you leave a UFO untouched, you will get penalty points. However, if all your fighters are shot down during combat with stronger UFOs, you will not only get a penalty for your losses and for the UFO, you won't have any fighters left to take on the smaller UFO's that might come later on to get some points back.
You need to research the weapon artifacts of each active race in the game to start the research-script of your weapon-research-tree. The same goes with autopsies/armor and defense-technology.