Forbes did a story on 5 ways leaders can be more likeable on social media, but the advice really doesn't just extend to leadership. The tips, along with some of ours, are easy ways to seem more approachable while posting. This is for individuals posting and not the company page.
#1 Be yourself.
The first simple truth is to let your natural voice come out. Some people naturally let their comedic side come out. But if you aren't funny naturally, don't try to force jokes on Twitter. It will come out feeling forced.
#2 Be vulnerable.
Acknowledge mistakes that you make. Let people in when you are mourning someone. Don't be afraid to let people care about you. Social media is not just "PR" posts but is about letting people know who you are.
#3 Be aware that you represent not just you but your brand.
While you should be yourself, be aware that to the public, that self represents whatever company you affiliate with. So while you may individually have a strong opinion about something, if your company doesn't, you may want to rethink the post. Or be very explicit that you speak for yourself and in no way represent the brand. But that usually backfires.
#4 Be polite. There are a lot of abrasive people on the Internet and it is very likely they will share their negative opinion to you. That doesn't mean you have to engage. Getting into a Twitter-war may be OK if you are a huge celebrity but for many that also represent a company, it just ends up reflecting poorly on you.
#5 Don't be an advertising wall. Yes, you can occasionally mention your company or some cool deal but if you are just the guy selling Ray-bans on Facebook, you are going to get reported as spam. Have fun and lighten up. Post a funny cartoon that made you chuckle. Post about trending events. Don't just push your product.