For this getting started guide, I will assume you have created a "New Geo", and not "New Tactical".
Your first task of business is to build a base. To do this, click/tap on the bottom left button on the screen.
Next, click/tap where you want to build your base. You may want to consider each region's traits. Africa or Asia, near the equator and away from cities, is often a good choice.
Your next base will be much more expensive, but it is recommended that you build a second base immediately with at least missiles to help you ward off at least part of the alien spacecraft. To build your second base, you follow the same process as the first, but note that it is not equipped, so click/tap on your Bravo base (2nd base), and click/tap on "build" on the pop-up menu. This will show you the base where you can build an assortment of structures.
The aliens will come very soon into your game (possibly even before you've built your first or second base). If you've built your first base (you have scientists), you'll be able to research their arrival by clicking on the beaker on the top left button on the screen.
It is useful to check periodically on which research is being done, as you may want your scientists to rather work on something else.
If your base has shot down an alien craft, or they have landed to close proximity to your first base, you will be able to click/tap on the alien craft to initiate an investigation team to the alien craft. Downed alien craft stays on the map for a fair while before it disappears, but crafts that landed needs to be investigated as soon as they land, otherwise you will lose a control point (check name of this?) in the country that the ship landed in.
Once your investigation team has reached the alien craft the game will switch to tactical mode.