Send out 3 social messages as you go about your day and ask others about theirs.
I know you may feel uncomfortable sharing what you see as personal or pointless information, but the fact is it part of engaging with people. You can comment about the weather, a successful meeting you've had, being stuck in a traffic jam ... It really doesn't matter what it is and you don't have to give away any deeply personal information. You just have to engage.
Share 3 things you have found that you want to share with others.
This might be a bit of news, a link to a blog, something you’ve learnt, a bargain, a review .... the list is endless and the choice is yours. As you become more experienced you will learn what your followers are interested in. As a Confidence and Career Coach - I often share things I've seen related to coaching, but not exclusively so.
Retweet 3 messages from other people that you think are worth sharing.
It's really imortant when you use Twitter that you just don't promote your own brand. Some people put out some very useful information, so when you come across it - share it with your followers. The more you do this people will also return the favour for you. Make sure that you have checked out what you're retweeting or you could be sharing poor quality information.
If people have a schedule of Tweet tasks daily as you have laid out, I definitely think they will be able to spend 20 minutes during their day and forget about it (other than responding to @mentions).
An automation training piece would be a nice follow-up to this, using a service like Tweet Deck. It can become a quick "weekly" task if this is done correctly. :) Thanks again.