Si is essentially concrete and detail-oriented. A person with primary Si, say ISFJ or ISTJ, is often very good at noticing and organizing the details -- they remember dates and names, they excel at categorizing information, and they can organize and process facts like it's nobodies business. ISFJs, for instance, have a great knack for interior design and office work. Because of this, they end up relying a lot on their organization, which ends up turning into a routine. They are geared towards remembering things and steps that worked in the past, which is why tradition becomes so important. It works, and you don't fix what already works. Si is grounded, but because of that it is also a bit stubborn.
In auxiliary, it is fairly similar, except a little downplayed. Kind of like the difference between INFJ and ENFJ -- it's still there as the dominant perceiving function, but the extroversion comes first. So an ESFJ might be a very good secretary or other human relations worker.
Tertiary Si, in ISxPs, appears as a sort of grounding in their personal values, in my opinion -- their Ne works to think of possibilities, and their Si looks at their storehouse of data and facts to compare how well such-and-such a concept might have worked in the past. If you notice an INTP, for instance, they may come up with a lot of different theories, but at the same token, they can be rather amazing at finding the odd facts to support them.
Inferior: ENxPs. These are less obvious. If a ENxP is pushed a lot or in crisis situations, especially, you'll notice they tend to become more obsessed over the little details and bits of organization. That's Si at work. I'll admit, I don't know as much about this one.
Se is different. Se is about the world around you in the present moment. It can seem a little ADHD at times. It's about experiencing the world and the physical sensation of it, and of being aware of all that that involves. For primary users, ESxPs, this often appears as a great knack for things like sports and physical activities, or it can show for a love for all things "new" or interesting: the next fad, the next sensation. Whatever is exciting and stimulating.
For auxiliary, it's a little different. Se is not just about sports and physical activity -- it's also about being absorbed in the moment or the activity. Hence, ISTPs are often known as the mechanics, and ISFPs are known as the artists. These people can get into a project with all of their being; they are drawn into the physical trance of it. Drawing, painting, music, tinkering with an object, whatever makes you totally absorbed in an activity -- that's Se. They often don't finish their projects, though -- it's about the moment and the doing, not really so much about the final result.
In tertiary, ENxJs, Se appears as a motivation to do. ENxJs often use physical exercise to relieve stress, and they are often very excitable when they have something to concentrate on and work towards. They are more in the moment than their INxJ counterparts because their Se is closer in balance with their Ni.
Finally, inferior Se users are INxJs. Se appears either later in life or when stressed or pushed, usually. INxJs are known to really take charge in crisis situations -- that's Se at work. I recommend trying to work with Se to help balance Ni -- when used correctly, it can really help ground INxJ types.