If you have some unused STEEM tokens in your steemit account that you don't want to spend powering up your Steem Power or have earned some Steem Dollars from posting good articles and you want to withdraw them to Poloniex here is how you can do it.
First login to your Poloniex.com account, got to the Deposits and Withdraws page and click on the Deposit link on the right to either STEEM or SBD (Steem Dollars).
What you will see is a unique Your STEEM Memo ID generated that you will need for the transaction to go through, take a note of the string you got and move on to your steemit account.
Open up your Profile page on steemit.com and go to Wallet then click on either the STEEM Balance or Stemm Dollars Balance on the right and choose Transfer.
You will get a window popping up with a few fields that you need to fill in:
The To field needs to be filled with poloniex as you are sending your Steem there
The Amount field is for how many STEEM or Steem Dollars you want to send
The dropdown box allows you to switch between STEEM and Steem Dollars (SBD)
The Memo field is where you need to type in the ID you got generated at Poloniex when you initiated the deposit request
Just click on Transfer and in a bit the STEEM or Steem Dollars should appear in your account on Poloniex where you can trade them
Do note that STEEM POWER is not transferable like STEEM or Steem Dollars are!