Your setting will have policies and procedures for everyone in the setting. Ask for copies to read.
As well as staff (or any adults visitors) following health and safety procedures, you will be teaching the children about health and safety - washing hands/snacks/lunch/safety of themselves and others such as you may ask them not to run inside but explain there is plenty of room when playing outdoors. You will teach them how to stay safe - perhaps through age appropriate talks and stories - crossing the road, not running off, how to protect themselves if they feel vulnerable.
Practitioners will have training -ongoing and refreshers, in-house training and staff meetings etc. You will have staff that hold first aid certificates/handling food certificates; you will hold regular fire drills. Your setting may have all electrical appliances checked annually.
Your manager or supervisor will ensure that everyone knows their role and responsibilities to ensure that every health and safety precaution/procedure is followed. All staff (as responsible adults) should check/monitor that everyone/thing is safe. Child illness - you will have a policy on that - do you allow contagious children to attend? if not ? why not? - health issues.
What do you do if a child has a notifiable illness - do you know the procedure to follow then?
You will have many risk assessments that you carry out daily to check that the outdoor area is safe from 'foreign objects' and that all gates etc locked, what is your visitor policy like? how do you keep the children safe?
What do you do if you feel a child is in danger ?- i.e. picked by an adult who appears to be under the influence of drink/drugs/solvents?
What do you check when you open up? Who is in charge of what? making sure toilets are cleaned, undoing the fire doors etc
The list is endless, but check out your policies and procedures and it should all be there.
Policies and procedures should be checked on a regular basis (at least annually) to ensure that everything is in order - or added to adapted or changed as and when needed.
There will be many more health and safety issues to consider, but start with your policies.
I hope this helps get you started.