I went through all this about 15 years ago when I first started doing the sort of job where I sometimes needed to fire people. If you’re basically a ‘nice’ person, it can feel very awkward to have to do this.
Try to see the bigger picture. If she isn’t right for the job, and the job isn’t right for her, then it’s in everybody’s interest, including her own, to terminate the job. Anything else is just postponing the inevitable. While the current situation persists, she’s making herself stressed and miserable by trying to cope with a job she isn’t cut out for, the company is losing out (by having to compensate for her failings), and you’re losing out by trying to manage someone who isn’t in the right position. There’s another, invisible, person involved: the worker who is looking for a job, who would do this job really well, and who is keen to work for you and produce good results… but whom you can’t employ until this current worker is fired.
I am assuming you are fully aware of the legalities of firing someone, and you know what you can and cannot say, or discuss. There are all sorts of relevant laws and there will probably be a company policy on the matter. Make sure you know this stuff before you go ahead. There can be very serious repercussions if you say or do the wrong thing.
In the light of the relevant legislation and policies, there may not be much that you can actually say. However, IF you are both able and willing to actually have a conversation about it, then there are some good rules of thumb. Don’t make it sound like ‘You’re a bad person’. She isn’t. Don’t make it sound like ‘You have failed’. She has, to some extent, but no more than the person who appointed her to do this job, and it isn’t the right emphasis. A good line to take, if you have to take one, is ‘There’s nothing wrong with you, and there’s nothing wrong with the company. But we aren’t right for you, and you aren’t right for us. That’s all there is to it. Sometimes these things work out, sometimes they don’t. You’ll move on and find something that’s better for you, where you can thrive and prosper. We can help you look, and we can give you good references that will help you’.
Also, even though it may feel harsh, be 100% positive and clear that her employment IS being terminated and NO, there is no pleading or negotiation involved. Some employees start to argue or plead their case, and if you waver at all you are just prolonging the process and extending false hope. It’s a ‘be cruel to be kind’ sort of thing. Be clear, be definite, let her know FOR SURE that this IS a final decision and there are no alternatives to discuss.
Try to have someone else present, on your side of the fence. It will be good for you, it may be legally important to have a witness, and it will help to underline that begging/pleading isn’t going to make any difference.
Observe the niceties where you can. Think it through in advance and see how dignified you can make this process for her. Will she have to empty her desk and so on in front of everyone else, or can it be done at a time when there are few other people around? Can you spare her any humiliation or embarassment? Can you make her feel that although this job didn’t work out, you actually like her as a person, and want to be as considerate as possible?
If you can offer her any realistic help towards finding a new job, then do so and make it clear that you do intend to help. It’s a nice thing to do, and though she may not warm to the offer at the time because she’s too upset, in the days or weeks ahead she may actually value your help. But don’t mention this kind of help if it’s not honest and realistic.
Finally, as in this situation as in life in general… don’t burn any bridges you don’t have to. I have seen at least two situations where a company fired someone only to find, later, that they needed this person’s help, passwords or co-operation. Difficult situation! Proceed with caution. And remember that an ex-employee can spread an awful lot of bile and nasty rumours about you and your company, if they so choose and if they feel badly done by. I’ve seen this happen, and it can get very serious.