The strange sensation may make you want to cough at first, but just stay with it, it becomes less awkward after the first second or two. Once you have done it once or twice it really is pretty easy and actually feels good!
As you come to the end, stop pouring the water through your sinuses and slowly bring your head upright again after all the water has drained out. Give some quick blows through your nose to clear things out and check out what's in the sink below. The first time I did this some big stuff came out, after that, I really have to much "nasal debris".
Take a second to compose yourself, refill your Neti Pot if you are running low on saline, and then switch nostrils and repeat the process. When you've finished pouring in the second nostril, blow air out through your nose in a few quick short breaths to clear out any water. You can also put your head down towards the ground to drain out any remaining water.
This is a video of me doing it for the first time ever - so I am a little surprised as to how it feels to pour water through my sinuses.
I don't think that it's possible to overdose on Neti Potting, so do it as often as you like. I know lots of people that do this as a preventative activity every day.
Enjoy your clean sinuses!