Hi Edd,
As previous replies, depends which organisation your entering, hopefully you would have done your research on their Health and Safety Culture previously.
For me theres usually 3 courses of attack,
1. Human input and Behaviours, and,
2. Compliance with legislation, and,
3. Safety History, any safety data, responses to accidents and implementation of improvements following accidents, and, any safety suggestions.
Personally ive found no 1 to give me the most feedback on 'where the company is now' to develop 'where do we want to be' and most importantly 'how do we get there', data is generally created from one persons interpretation of and incident/occurance and can sometimes be a biased opinion on the truth, speaking, listening and responding to employees (at all levels) will most definately help you form some of your own opinions without bias (except your own of course).
So I would say
30 days - review data, spend time with employees (all levels), record findings (for yoruself)
60 days - Develop plan of action - include feedback from all levels, share with key H&S stakeholders - adjust and publish
90 days - Form implementation team (if required), include safety 'champions', sign off by senior Directors, develop measurements for success.
Measurements possibly: reduced accidents, greater employee input (more feedback, higher near miss reporting etc).
just some of my ideas I have used myself (including a new role this year!) hope there usefull for you, obviously this requires more depth, happy to help and good luck (if its yourself).