We have relatively older recessed lighting in the basement. Very dim and not functional. If we were to replace the existing lighting with more brighter modern modern lighting that would make a world of difference,. My question is my level or experience is minimal. White to white green to free etc. how difficult would it be to replace the existing lighting my self. Is it a matter of shutting off power and dismantling and reconnecting? Or is it more involved like running new wires and lines and such? Could it be as simple as out with the old and in with the new?

It could be a fairly simple in and out, depending wn what you have in there. The really old stuff may not have a ground and/or the romex can be cloth covered (which is surely shot by now).

Hardest part is fitting the new cans - you may have some drywall patching to do.

what kind of older recessed lighting? if it's standard 6 inch cans, they can be retrofitted with LED lighting that mounts on the entrance of the can. that would distribute the light wider. several manufacturers make that stuff, no removal needed, it's screwing a cable with an Edison base in and setting the LED surface at the edge of the can with the ones I've seen.

give or take $50 each, but at that price, it's worth trying one to see if it makes a difference in a particularly dark corner. if so, the retrofits will be cheaper than opening up the ceiling, removing, rewiring to code, and putting up a new ceiling.

will cut your power bill down there, too. but it won't work if you have troffer fluorescent lighting, that's going to require heavier remodelling.