I've been on both sides.
1. Understand that if you're in a situation where you have to fire someone, as the manager, it is and was your fault. Your fault for not seeing at the beginning that it wasn't a fit, or your fault for taking someone who had potential and then alienating/de-motivating them along the way. Only with this mindset can you learn not to repeat the same mistake. It's all too easy to just chalk things up to "they were a bad employee" - there are certainly cases where it's not your fault, but I think people tend to vastly underestimate the number of cases where you actually could have changed the outcome.
2. Whether or not the situation turns ugly is up to you.
Fire someone unexpectedly and without serious efforts to try to help him/her = possibly ugly. Diplomatically try and help someone work through their issues and only then after a few weeks bring up to issue of them leaving = possibly not ugly.
Fire someone who has a 1 year equity cliff after 9 months on the job and give them nothing = ugly. Fire someone who has a 1 year equity cliff after 9 months and give them 9 months of equity + $$ severance in return for signing a release (talk to your lawyer) = much less ugly.
3. Feelings vary and I don't have much to say about them.