Want to play for free? You’ll want to upgrade your Molvernit, Metal, and Fuel refineries progressively so that the rates they produce materials increase. You can then use the materials to make and run ships you’ll use to take bases.
There are two ways to get production for free. One is to hover over a refinery and click in the strange box (mixed with triangles to prevent computer hacked clicking). The other is to build export freighters with your home base; every time you get to 10 freighters they will trade for 1 titanium. You can then use 1 titanium to get 1 hour production of Molvernit. Use that to upgrade your refineries. Next make 20 total freighters to get 2 titanium to get 1 hour Metal production. Keep going round after round of Molvenit production, refinery upgrades, Metal production (producing fuel and making freighters as needed to keep that going). IMPORTANT NOTE: Freighters will cost fuel and the price will go up as you produce them. However, the price is reset (daily, I think) down to 2,700 fuel, so when the price gets too high (like 10,000 fuel or something), just produce fuel and store it till the price is reset.
To take bases, you’ll want to start by going after very weak bases, which are the ones with only one cannon that's already down to 1-2%. The green arrow points to such bases to help free and noob players find them, but you can pick any base you want. A solid attack team for that weak of a base would be a few scouts of either type and then a couple of either Lipatro Class (good all around) or Penhalto (really good on base cannons, but not much else). One of either of those along with the scouts will likely also succeed but you might get some damage to your ships in the process. Be careful on your way there. If you get too close to an enemy base as you pass by it, its cannons will shoot at you. Once you are near the base you want to attack, prepare for conquest by producing a Conquest Ship which you’ll need to take the base (takes 45,000 metal). Then, select your attack ships and click on the center of the target base. Once the cannon is destroyed, carefully send in the conquest ship and you will have the base.
To protect the base once you have it, set up more cannons. Four is probably a minimum, but it could still be retaken by someone with higher power ships.
Want to buy titanium and play at a higher level? [I will expand this section and add a lot more stuff by request. If you want more explanations on basics, let me know. To do that, hover over the "about" in the website header and you'll see a "contact" link.]