If you wanna use some nice and free Fonts then you should try Google Fonts Family, Here you will find some nice collection of web fonts which can be used on your web page and its too without any kind of restriction.
If you wanna use those Google Fonts on your web page then here is a quick way to do so, first you need to select which Font you wanna use for your web page, once you had selected your Font just paste the following line inside your <head> section :-
<link href=’http://fonts.googleapis.com/css?family=Google-Web-Font-Name‘ rel=’stylesheet’ type=’text/css’>
Replace Google-Web-Font-Name with your selected font name, If you are using WordPress then you can import those Fonts via your Style file, for this you need to open your Style.CSS file and then paste the following code above any CSS definitions and below your Theme description.
/* Import Google Fonts */
@import url (http://fonts.googleapis.com/css?family=Google-Web-Font-Name)
And at last font where you wanna use it, like I had defined it to be used on Body of by theme :-
If you had followed all step correctly then you will get your Fonts on your web site.