We live in an increasingly Health and security informed environment and sometimes people complain about that, however it is hard to argue that taking sensible precautions is a good idea. I would suggest that the most fundamental of steps you can take is to ensure that at work there is a correctly stocked first aid kit. If you are in cost then it is your responsibility to supply one, if you are an worker you should be sure that you know where it is and what is in it.
The next most essential feature is to ensure that it is 'environment appropriate'. What I mean but that is that the kit has in it points that are most most likely to combat the hazzards faced at work. Most kits will have the same simple essentials (plasters, slings, similar) but if you are working with specific chemicals you may need eye baths, goggles etc. If you are working as a tree surgeon then you are more most likely to face dangerous accidents than you are if you are seated at a desk typing! Make sure that if you have an emergency the thing that you might need is included in the kit. A lot of firms stock specific workplace first aid kits specific jobs. It is a good idea to check these for what they have in them if you are not buying one directly.
Make sure that it is someone's job to keep it checked and stocked. There is no point in having a workplace first aid kits that has run out of plasters! At home you can keep easier track of it because you are probably to know who is using what, at work this may not be the case so it needs to be looked at regularly.
Finally make sure that you have sufficient workplace first aid trained workers on site and ensure that they are happy with the contents of the kit - there is no point in having one if the person needs something else every time or has no idea how to use the contents.
Hopefully you will certainly not need your first aid kit in the workplace. But if you do it's best to be prepared.