1) Snatch up unowned blogs. Got artefacts? Use them. Go through the industries on your arte list, searching them for unowned blogs (I find Firefox's "find" function particularly useful for this). Hit them with a pressure public to buy the shares at one third of the normal price (if they're above P/E 60, PRD them first. No-one owns them, so no-one will care).
I've been doing a lot of this recently, packaging them up into parcels of a billion B$, and passing them on. I'll have another lot ready in a week or two, BTW, so if anybody wants it (who hasn't already had such a package), drop me a line.
2) Loot the dead. Look for players who have not logged in for a while (I have a list), and use your artefacts to ream out their portfolios. For this sort of thing, I tend to PRD until the P/E is < 40, then restructure and HTO. Again, they're dead, so no-one will mind.
3) If you prefer a more vigorous style of play, look for high value blogs with low P/E and steal them with restructure and HTO. They may be stolen back, or they might not be, but you'll probably make a profit. Try to avoid "friendly fire" while doing this, and remember not to steal from Robber Barons or their ex-members who are still abiding by the truce.
A good thing to do here is maintain a dead list, and sort by P/E. I do this with a folder called "Reposessed" - basically those high-value blogs which have passed through my portfolio in the past. Every time I log on, I check to see whether anything is at the top, and steal it. Most gets taken back, but its a constant source of revenue.
4) You can also loot the living, but this tends to upset people. At the moment, I'm trying to avoid doing it too much, except on the ultra-high-value (B$1,000,000+) blogs, where its a great way of making money.
Note that all of these are artefact-based strategies - so if you don't have any artes, acquire some. The cheap ones are well worth it. The expensive ones (those with ideas valued at over B$1000) don't really (or at least not through shares play), and are of interest mainly for ideas play and collectors.
Also note that the daily transaction limit doesn't apply to artefact play, so once you've made your 20 buy / sells, you can use artefacts to your heart's content to build your portfolio.
Idiot Savant is an excellent shares player, and has amassed a portfolio worth B$ 11.5 billion. You would do well to follow his advice.