It's pretty much left up to the individual GM.
All IMTU . . .
I have it so that most orders are medium-tough to get into, but there is still great disparity in difficulty.
In addition, there are some orders which can only be entered under very specific conditions. Like, the Order of of the Conqueror, a Knighthood (and IM military decoration, too) granted to the commander of a successful world-level invasion/conquest. (Not granted often 1110 Era.) If you aren't an IM commander who led a successful invasion, you can forget ever entering this order. It is also an example of a Knighthood that is awarded automatical on receipt of a military honor.
I've debated over whether the SEH should come with some order of Knighthood, but so far have decided against it for the moment (this goes along with a personal dislike of the 3-award system, MCUF, MCG, SEH, I alway thought there should be more to it than that).
The primary requirement for entry into most Knighthoods is sponsorship. Someone who is already a Knight of the Order or a high-ranking noble, like a subsector or sector Duke (or someone who is capable of influencing them), may think that a particular sophont is worthy of joining a particular order of Knights. They arrange to contact the leadership of that order, and provide an official Petition of Sponsorship. The leadership of the order reviews the petition, and decides whether or not to accept. There can be all sorts of tests to be passed and requirements to be met. The process might well be lengthy, and could involve lots of "Travelling"! The Emperor can create Knights in any order at will (usually abiding by the requirements of the order). Archdukes may create knights in the order of their domain at will.
The primary trigger to sponsorship is getting noticed by someone who is capable of providing (one way or another) a Petition of Sponsorship, or by the Emperor or an Archduke. The first, although quite difficult, is much easier than the last.
One can be awesomely heroic, win multiple SEH's on the field of battle, but if those "on high" don't deign to notice, there is no elevation as Knight. (With a few exceptions, like receipt of the Order of the Conquerer military honor, but that level is always handled by the Emperor's Office, anyway, so it can be considered as being noticed by those "on high".)
Some orders have no official organization charter (like the order of the Rose & Silk, an Imperium-wide non-military order of artisans, writers, poets, etc.), and therefore no specific leadership. Petitions of Sponsorship must go through the Office of the Emperor, where the review of the Petition is handled by a staff of nobles delegated to the purpose, with final authorization under the signature of the Emperor should the individual be accepted.