On Google finance, if it says a stock has a Div/yield of 0.35/2.58, what exactly does this mean?

It means the current dividend is $0.35 per share, so if you own 100 shares of the stock you are getting $35 from the company every three months. The yield is calculated by taking what you would receive in a year, in this case 0.35 x 4 = $1.40, dividing that value by the price per share, then multiplying by 100 to get turn the fraction into a percentage. Some words of warning about these figures: First, the amount of the dividend can change at any time. If you look at the dividend history for PNC at http://finance.yahoo.com/q/hp?s=PNC&a=08&b=7&c=1988&d=11&e=1&f=2011&g=v the dividend has only been $0.35 for nine months. Prior to that it was $0.10 for two years, and prior to that (before the financial meltdown) it was $0.66. Second, if you look at the same thing from a different source you are likely to get different numbers. For example if you look at Yahoo http://finance.yahoo.com/q?s=pnc you will see "Div & Yield: 1.40 (2.80%)" where $1.40 is the current yearly dividend (four quarterly dividends) and 2.80% was calculated using a slightly different stock price. <<<So does that mean the div/yield is 0.35/2.58= 0.1356?>>> No. the virgule (slash) simply was used to separate the numbers. It does not mean division.

It means that it pays a 35 cent dividend and the yearly dividend divided by the closing price of the stock is 2.58%

Div is the money you will recieve per share per year. In your case, $0.35 per share per year. Payable quarterly. 2.58 is the yield, meaning the % return in terms of dividend. In your case, ($0.35 / 2.58) x 100 = $13.56. That's the current trading price for your stock.