Be Organized, Focused, and Realistic
It is just common sense, but make sure to be organized, focused and realistic. This is extremely important in severance negotiation (and otherwise). Toward organizing your thoughts - and being focused - it may very well be helpful to write out your points before saying them.
If the Employer has delivered a severance agreement to you during your employment - or verbally advised you that they want you to consider severance (rather than continuing your employment) - but the Employer has not advised that they are terminating your employment, this is a special situation in which different opportunities and dangers are presented. Again, not to be a broken record, but this is a situation where you very well may want to consult with an attorney to explore your options and best protect your rights.
It is more difficult to get more severance in a lay-off situation (since presumably the Employer is offering severance to a group of employees according to a set formula), but it might be a situation where a good argument can be made that you should not have been selected for lay-off (and that it only occurred due to discrimination/ retaliation, or contrary to the Employer’s seniority/ selection process).
If, by chance, you are okay with the monetary terms of the severance, but have issues with non-monetary terms (for example language issues), let the Employer know this. Generally the Employer’s biggest concern is that you want more monetary severance, and by stating that you do not want more monetary severance (if that is the case) then that may very well open the Employer up to having a more successful and productive dialog with you.
If you are negotiating on your own - again, not advisable (as the Employer who has likely just fired you will not respect you or fear you acting by yourself without an attorney) - hen when negotiating be focused on what is most important to you and what are your main concerns. Also, do not negotiate when you are in shock or if you feel overwhelmed, and instead try to negotiate from strength not weakness. Think what are your strongest/ weakest arguments, and what are the Employer’s vulnerabilities. It may be a good idea to write this out, rehearse what you are planning on saying in front of a family member or a trusted friend (whose feedback you value), and have what you wrote out in front of you when speaking with/ calling the Employer.
Lastly, in this regard, note that if you first try on your own (without an attorney) to negotiate with the Employer - and you give a counter-proposal to the Employer’s initial severance offer - and it doesn’t go well, then from past experience I know that it is that much more difficult for me to get a maximized good result for you. One reason for this is that you have shown weakness by switching gears, and the other is that I may very well have given a larger initial counter-proposal but I may be constrained to some degree by the lower initial counter-proposal that you gave.