Being very organised is key. In all my jobs I have a system where the first half hour and last half hour of the day is devoted to email and task management - going through inbox, deleting junk, and assigning all tasks/incoming requests to one of 4 colour coded/flagged categories - 'urgent and important', 'important but not urgent', 'urgent but not important', 'not urgent and not important'. If you didn't complete all your tasks the previous day every day- you also need to review yesterday's task list and add in anything not completed and move things around, e.g. the thing which was important but not urgent yesterday may have become urgent by today (looming deadline for instance). At the same time I'm doing this I fire off brief acknowledgement emails to anyone who has contacted me/wants something, giving a timeframe for a response - usually within 24 hours if urgent, whenever I know I can find time for the non urgent. So everyone knows where they stand.
The rest of the time is blocked out and pre-booked in my diary - (1) meetings (although if you have more work than you have time for you need to be very ruthless about your attendance at non essential meetings), (2) time to complete urgent and important work and (3) time to complete other work, in priority order: first Important but not urgent, second urgent but not important, third non urgent non important (to be honest I never get around to the last category, I count it as being things like filing, reading through things I'm sent 'for information', reading my professional body's journal etc etc). How much time I have available to do non-urgent work dictates the timescales I've told people to expect said non urgent work. Certain tasks that I know come around regularly such as monthly reporting cycles, preparing for/chairing team meetings, boards, committees, 1 to 1s with my staff etc are booked out for the whole year in advance.
It's important to stick to your planned blocks of work, particularly the time assigned to important but non urgent work, it's quite tempting once you've finally cleared off everything which is urgent to sit back a bit, check your emails, maybe reply to a few, chat to colleagues etc in a way which you wouldn't if you knew you had to do something which was really urgent. But sticking strictly to the blocking out system is the only way that the non urgent work ever gets done - if you are able to switching off your phone, email and IMs/showing yourself as 'do not disturb' helps.
Obviously the hard thing is knowing how to categorise things in particular if you are getting external pressure (something a client or colleague thinks is really important may not actually be), and also of course re-prioritising if when things shift around and previously things no-one cared about are suddenly top of the agenda is stressful too. But I think if you can get broad guidance from your manager (e.g. anything which effects a customer/delivery of key objectives is automatically important no matter what, anything which will cost the company money is automatically urgent) that will help, and also where you need to set deadlines which are longer than people will like, having this system will help you get back up from your manager, so you can say 'I have had to say to Colleague A that they won't get their report until next week, this is because I have tasks BCD that are all urgent and important for XYZ reasons and will take 10 hours to complete, the next available time I have to complete the report is Monday, unless you are able to say tasks XYZ can be delayed or I can have help completing them' - rather than saying 'I can't do colleague A's report, I have too much else to do' which as a manager is not that helpful to hear....