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Found a couple of articles written by members of the community. Having more than one article and no "official" sanction makes me hesitate. What if one is not correct and following Murphy's law it is the one I unwittingly choose to follow? I would have expected some kind of official, step-by-step simple instruction manual.
Then there this "power up" process which is not clear how it works ...
Ok, I'm going to work more ... I guess one needs to do some "proof of work" here as well :)

Regardless you have to be careful. You could try transferring in .001 steem and see if it works.

That's too little, the Poloniex transfer fee is 0.01. So the minimum amount could be something like 0.011 (since if I transfer less than that I might not even see it arriving in my Steem account).
After more than one hour the 2 transfers I've tried (one to MEMO one to ACTIVE) still didn't get through, still marked "Pending" on my Poloniex page ...

Have you looked into coinbase and bitrx?

Hi Sorin, I haven't used Poloniex, but I've used other exchanges, and I did transfer some STEEM from an exchange to steemit. Go to your wallet and click on Buy Steem or Steem Power. Another page will pop up and you'll see "Your receive address". The address is your username, but you'll also need a memo, which you can generate by clicking "Get deposit address". Then go to Poloniex and locate your Steem wallet. Click withdraw and when the next page pops up, insert your username as the address and then the memo in the memo line. Like mysearch is over said, you'll want to try a small deposit first. I sent 1 steem fist to make sure it was working. ...To your next question - Once your steem is in your steemit account, you can power up by going to your wallet. You'll see (amount you have) Steem with a down arrow beside it. Click the down arrow and from the drop down click "Power up". You can convert as many Steem into Steem Power as you want. For a description of what the different currencies are on steemit, I posted an article this morning on my page. I'm new here too, but feel free to ask me any questions and I'll try to answer.