I can only accurately answer this from the perspective of a consulting electrical engineer -- meaning someone that produces construction documents like blueprints and specifications. You are often juggling several projects at once and each is often in a different stage of development. The day might start with a meeting with a prospective client to pitch your firm's qualifications to see if they would be willing to hire you to design their new building. On the way back to the office, you might drop into a project under construction to do a "site observation" to see if the owner is getting what they paid for. Back at the office, you write up a report on that site visit and send to the owner of that project. It might include an "Engineer's Punch List" of items that you found were not meeting the contract.
The afternoon might include reviewing some submittals on a project to see if they meet the construction documents requirements. Then comes some time with the mouse in hand in front of a workstation where you make progress on a current design using AutoCAD and Excel. Answer a lot of emails and return phone calls are all in a day's work as well. These are a few of the things that might happen but there are many more. There's a lot of variety in the type of activities you do and the variety increases with your skills. Never a dull moment as a consulting engineer!