Explore the analytics section of your Twitter account. What sort of things did you find out?
Good question. I've been at the Twitter Analytics addictively since it appeared, and Georgina's post is valuable for urging me to explore the section more comprehensively. I can confirm the report by 'Librarian at heart' that tweets generally get more seen and more responded to if they have hashtags and pictures in them. And, in a subjective impression I haven't statistically confirmed, Twitter Analytics' list of my top tweets seems to have a lot of those other blue things in it -- links and Twitter handles.
The blue/popularity correlation reflects the experience of 'A waterfall of consciousness', that tweets did well when they reworked other tweets or combined subjects. I fear I cannot replicate that post's experience of success by a tweet "that tackled a controversial subject with a negative bent".
But it's gratifying to see that my own top tweets include this one:
Tnx Retford pharmacist, who didn't have my medication in stock so rang Retford's other pharmacists till one had it. Is this standard?
No blue text in that one; the tweet was presumably popular by the pharmacist's merit alone. Quite right.
Track a URL using TweetReach. Try experimenting using a URL from an existing tweet
I have signed up to TweetReach. I tracked the fortunes of a couple of hashtags I have tweeted about in the last week, but I can see I would need to be using Twitter more seriously before my use of this service became illuminating.
Add the Altmetric bookmarklet to your browser and test it out on some academic articles (either your own or from someone you know).
Use of this tool requires greater seriousness still. True, it will tell you how often things have been tweeted, but the things in question have to be, as noted the comment of 'Librarian at heart', of a kind to have a Digital Object Identifier before Altmetric will work. I got that, but I was slower to twig was that you had to have the article itself on the screen first -- the presence of a DOI wouldn't magically make an abstract or ResearchGate post Altmetricable.
For me, Altmetric would be a thing to recommend to researchers, not one that I'm likely to apply often to publications I have seen. Like the other tools surveyed in this post, Altmetric will tell you where a publication has been. It says less about what the publication did when it got there.