We made a hiring mistake and need to terminate an employee. It's one of the hardest things I've come across as this will be a first. What the best way to gently let go of someone who isn't the right cultural fit, but does have the skill set for the position.
The legalities are going to depend on your local law and any contract that may have been formed (and whether that's a written contract, or implied contract). You need proper legal advice for this.
Aside from the legalities there's a few things you should think about. For context, I grew up in the UK, now live in The Netherlands but worked as a manager (including hiring and firing many) for three years in California. The following steps are what I feel are reasonable in most situations where you're dealing with cultural/behavioural issues which don't fall under "fire them immediately" grounds. They are also how I would expect to be treated.
1) is the employee aware that there is a problem?
If the answer is "no" or "not really" or anything wishy washy, then stop what you're doing, right now and talk to them. Ask them how they think it's going. Ask them if there's anything they need help with. You should be doing this with all your team anyway.
If you fire someone and they are genuinely surprised to hear about it, you have failed as a leader.
2) have you given the employee suitable chance(s) to rectify the problem?
Talk to them about the desired cultural model, and explain that you are concerned that they might not fit, and ask them why that might be and whether they wish to continue. Set a reasonable expectation and ask them whether they can meet it - and what you can do to help them meet it. Then actively help them meet it.
If you let them fail by being passive, you have failed as a leader.
3) repeat steps 1 and 2
4) have a last chance meeting
Explain that things are becoming dire and that continuation down this path can only lead to termination of employment. Offer them support/help to fix the situation rapidly, or for them to move on voluntarily.
5) Fire them. (once you have legal advice).
Bring them into the office, by which time they should already know themselves why they are there. Tell them immediately that you are letting them go. Then tell them why. Keep it short and factual but empathetic. Do not allow bargaining, negotiation or any other pleading. It's done.
Document each step with a short memo (email will work) between you and the employee, covering what has been discussed and the agreed actions points (both sides). Keep copies of these and related communications safe.
This is the guide I always have in mind (I've let go a few people in the past).
1. Be grateful.
Just because I fire someone doesn't mean he/she has not done something well in the past. Thank him/her for his/her contributions to your company.
2. Stay objective.
I try to explain as much as possible that the reason is tied up to a certain skill set / performance that he/she was not able to perform. It should not go more personal than that.
3. Do not close out opportunities.
Point out his/her strengths that make him fit for other jobs that are available out there. You can go the extra mile by helping him/her land a job that fits the skill he/she already has.