If you are using MySQL version 4.1 or later, the answer is yes, you can have different character sets (e.g English and Russian -- cyrillic). You will need to visit the MySQL manual for your options. http://dev.mysql.com/doc/mysql/en/charset-charsets.html
Here is a CREATE TABLE for a table that I have created for translating holding both Russian and English. Notice my specification of UTF-8:
CREATE TABLE `EnglishRussian` (
`id` int(11) NOT NULL auto_increment,
`english` char(35) NOT NULL default '',
`russian` char(35) NOT NULL default '',
`vocabularyCategoryID` int(11) NOT NULL default '0',
PRIMARY KEY (`id`),
KEY `english` (`english`),
KEY `russian` (`russian`),
KEY `vocabularyCategoryID` (`vocabularyCategoryID`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
As far as what you need to do in your PHP/HTML form, you should try to set your meta charset to UTF-8 as I have done:
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
Hope this helped.