Unfortunately this is not a one-size-fits-all answer. The best day and time to post is going to depend on your target audience.
If your target audience is young stay-at-home mothers they are unlikely to be checking their social media first thing in the morning when they are trying to get kids ready for school, or anytime from 3pm (school pick up) to 7pm (bedtime – hopefully), but they may be active mid-morning, at lunchtime or later in the evening.
If your target audience is busy executives they are unlikely to be surfing Linked In first thing on Monday morning, when they have a pile of emails to go through, or on a Friday afternoon when they want to get finished and go home, but they might have time for a browse on Tuesdays at 10am or Thursday lunchtimes.
So….apart from using what you know about your target audience to guess, how can you really KNOW what time to post. My best suggestion is to use the data from Google Analytics (you got that set up when you launched your website – right?) to find out when people visit your website and this will give you great guidance as to when people are interested in finding out what you do. If you need more help with Google Analytics click here to read more
The final issue with social media timings are that you may end up scheduling posts whenever you have the time….solution to this is to use a scheduling tool (such as Hootsuite) to make sure posts go out at the best time for your audience, not for you.
Many of these tools also have a Auto Scheduler function, which in theory can choose the best day and time for your post – use with caution though…