You can use \oldstylenums{01234567890} for specific cases. However, some font packages such as mathpazo which is palatino have options to set this automatically for text so that you do not need to type in the command explicitly, so you simply load the package normally, for example for Palatino is:
\usepackage[sc,osf]{mathpazo}
You can see some working examples with various fonts in this question Palatino fonts and the number 713
One of the problems in setting oldstyle numerals globally is that they look wrong in tables with a lot of numbers. A good solution to this problem was provided by TH in the answers to the above question.
If your font does not have text figures built in; the textcomp package attempts to remedy this by effectively generating text figures from the currently-selected font.
Put \usepackage{textcomp} in your preamble. textcomp also allows you to use decimal points, properly formatted dollar signs, etc. within \oldstylenums{}.