The following hints are basics as well as a few more advanced tactics and strategies to get better results so to speak with your performance against others or the AI. The more advanced hints might spoil the fun to find out about themselves a bit, but I marked them text-wise below, they are at the bottom anyway so you can overread them if you like. It starts with some general game control hints first:

• Options menu bar is by default hidden. You need to move your mouse to the upper left edge of the screen to make it show up. There you can save and/or quit a game.
• Fleets can be selected by clicking on the race icon on galaxy map in the respective sector. Then on the lower panel on screen the available fleets and ships are shown. Three clicks are needed, first on galaxy map race symbol in the upper right corner of the sector in question, then one left-mouse-click on the ship/fleet in fleet panel below on screen, then on the sector you wish to fly into.
• Outposts can be build by transport class ships, just go over the order buttons on bottom right after selecting such a ship, you'll find the correspondingly-named button there. After finishing an outpost, (an)other transporter(s) can even upgrade this outpost to a full starbase by essentially clicking on the same button again for this ship
• After meeting another alien race (mostly a minor, major homeworlds are not supposed to be close to each other at game start, but it can happen), you can set up diplomatic relationships with this minor. If he is in favor of you, i.e. neutral and above, try to convince him to sign a trade treaty with you. Once accepted, lay a trade route to his homeworld.
  In order to do that, go to system->trade menu and click on trade routes (use your homeworld as starting point first, could be you need to wait a few turns into the game before a trade route is allowed population-wise, you'll get a note however in-game about that), then lay it to the sector in question. After that you'll have the benefit of evergrowing relationship values with this minor. It is slow, but overtime you will see that he becomes more and more friendly towards you (depending on his race traits of course, not all minors act the same way) and eventually offers you better treaties and at last membership.
  Trade routes can be laid to other majors as well when you have a trade treaty or higher with this major (non-aggressive pact does not count here). Since majors mostly got more than one star system under their control, you can lay a full set of trade routes towards their systems (1:1 relationship there, so 1 sector to 1 other sector). Income from that route is calculated by both systems' population so it helps when you have some intel about their system pop. Cancelling a trade route works the same way as laying a trade route, you'll notice it becomes pink on galaxy map and ends in 5 turns.Then you can for example retry to lay a more profitable route if you choose a wrong one the last time (so to sum it up, try to lay evenly routes, i.e. a 30bn. star system should do trade with a 30bn. star system of another alien race and so on, having a 50bn. system doing trade with a 10bn. system is a bit of a waste of credits).
• Use resource routes right from the start after you colonized your first world. Most likely it will need titanium for its structures to build and your homeworld has more than enough at the beginning. Resource routes are laid similar to trade routes but work resource-wise, so just one resource per route is possible. Also I would not recommend laying more than one route per system since only one route is for free, more than one go at the cost of trade routes, i.e. for each further resource route you can lay one less trade route from that system.
• Diplomacy works as follows: Once you get to know / meet another race, it is added to your diplomatic menu in the list at left hand side. You can click on it and see how this race is seeing you (hostile, friendly, optimistic, etc.). By giving gifts you can try to improve your relationships with them. Once they are neutral or higher towards you, you may want to consider offering them a trade treaty. Once accepted, you can lay a trade route towards that race's home system. This gains you money/credits and continuously but slowly improves relationship with them. You can also bribe them if they already belong to another major or have higher treaties with another major.
  This holds for the "minors" in-game. A "major" is a race that can be played by humans or AI. These majors expand their territory just like you and they have slightly different diplomatic options, but in the end it should be self-explanatory what a "non-aggressiveness"-pact means and what effects an affiliation or a defence pact with another major race has.

Here some more advanced hints start, you may wanna find out about them yourself (you can get behind it yourself certainly, they are pretty logical when you think about it ):

• Helping minors terraform their planetary system helps increasing your popularity with them too. That way it can boost relationsships even from hostile towards neutral or above and then you can do as mentioned above to get that minor into your empire.
• I'd only terraform planets that do not take more than 10 turns at the beginning as a general hint. Also, multiple colonization in one star system boosts population number - though it costs of course a lot to build that second colony ship and works only if there are more than 1 planet in that system and that other planet(s) need(s) to be unterraformed, otherwise it gets colonized too by the first ship colonizing this world - is a thing worth thinking about. When you have >7bn. population in a system, you can build a so-called star-dock. This orbital structure increases range of your fleet and is one of the most useful things at early-game alongside researching engine tech towards level 3 at 100% RP allocation, ignoring the rest a bit because engine tech also increases maximum range of your ships making it possible to colonize and explore worlds that could not be reached before (or only when building expensive outposts to get there).
• I'd rather not invest too much credits into convincing minors at the beginning, buying colony and transport ships is IMO a bit more useful, but there are several ways to play the game (also depending on the race you choose to play with of course, each has its own special prowess), I just mention my way here.

Btw. it is "allowed" to take screencaptures from in-game, maybe even create a trailer if you know how to do such stuff. Having a gameplay video surely helps people see quickly what the game is like, more so than just screenshots. Also it can help explain game control issues like the ones mentioned above when taking short clips for each issue.