To get interest on money held in your Turkish bank you must ensure that your money is in a deposit account. Money left in your day-to-day "current" account does not (usually) make any interest.
I strongly recommend that you take advantage of on-line banking for deposit transactions, as the process is very simple once you're familiar. Nearly all the big Turkish banks have efficient English online banking systems which they will happily help you set up.
Fixed-term Deposit Accounts
These interest accounts are sometimes called "e-deposit", or "time-deposit" accounts. They work just like fixed-term interest accounts in the UK - you decide the length of time you wish to invest, which determines an interest rate. If you do not touch your money for the length of the term, you get your initial money, plus the interest. If you touch your money during the term you will forfeit the interest for that term (more below).
How it Works in Practice:
Interest rates vary depending on the term (length of time you invest), usually there is a good peak interest rate for a 30 day term. So if you were to open a deposit account on the 1st March, with a 30 day term, on the 31st March, the term ends and the interest is either paid out to your current account, or is left to accumulate in the deposit account. Deposit accounts usually automatically renew for the same term again - i.e. a new 30 day term will automatically start, however they will renew at the then current interest rate - not the rate you got the first time around. Note that deposit accounts can be started on any day, and can usually mature on any day apart from a Sunday.
If you decide that you need to take money out of the deposit account part way through a term, this is not a problem, you simply close the deposit account (the money will go back into your current account), note that you will lose any interest gained. You can then instantly re-invest the money back into a new deposit account.
A Note About Interest Rates
Interest rates are usually dependant on several factors, most importantly - the length of term, the amount invested, and the currency. TL will attract a much higher interest rate than GBP, EUR or USD. Rates quoted are usually pre-tax - tax on money in interest rates is applied at source, automatically by the bank, so expect to see about a 2-3% reduction. Interest rates are also per annum - so as a rough guide, divide the amount by 12 to get a monthly interest. Note that this is a vastly over-simplified model - and should not be taken as any form of financial advice - I advise you to seek professional advice before making any decisions regarding your finances
Latest Interest rates
Current Turkish internet e-deposit interest rates are tracked each issue of the Bodrum Bulletin. Visit our interest rate page here: http://www.bodrumbulletin.com/community/finance/889-turkish-interest-rate-report. You may also want to read the article regarding historical rates, here.