DG,
When you build a TR, it will stay in orbit (unloaded) in its home system. If you click on its star, there will be a sidebar panel on the right showing its planets and, at the bottom, a small box with all the ships in orbit. Click on the TR and you can load it.
The load panel will default to 50% of the system's population, or 50% of the TR's capacity, whichever is less. (This is what will be embarked should you auto-launch ships upon completion from the planetary screen.) You can adjust the slider to put however many soldiers you want on board. Once you are done, you can click on the small box marked "Launch" in the upper-right corner of this panel to deploy your TR one hex outside (adjacent) to your system.
Soldiers are just a part of your population. You simply lower your Pop when you embark them.
In the Military tech path, there are discoveries which give you +10 Soldiering. There are also anomalies which a survey ship can grab that will raise this stat +1. Soldiering bonuses give you better DRM's on combat resolution during invasions.
To invade, just move all your TR's in a group to the enemy star. (Group them to move all as one unit, so you don't invade piecemeal.) Enter it, and you will get a popup showing the range of odds. Press the spacebar and combat will be resolved.
~SDC~
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