Select user having qualifying data on multiple rows in the wp_usermeta table

I would use this query:

SELECT
  user_id
FROM
  wp_usermeta 
WHERE 
  (meta_key = 'first_name' AND meta_value = '$us_name') OR 
  (meta_key = 'yearofpassing' AND meta_value = '$us_yearselect') OR 
  (meta_key = 'u_city' AND meta_value = '$us_reg') OR
  (meta_key = 'us_course' AND meta_value = '$us_course')
GROUP BY
  user_id
HAVING
  COUNT(DISTINCT meta_key)=4

this will select all user_id that meets all four conditions.

@fthiella 's solution is very elegant.

If in future you want show more than user_id you could use joins, and there in one line could be all data you need.

If you want to use AND conditions, and the conditions are in multiple lines in your table, you can use JOINS example:

SELECT `w_name`.`user_id` 
     FROM `wp_usermeta` as `w_name`
     JOIN `wp_usermeta` as `w_year` ON `w_name`.`user_id`=`w_year`.`user_id` 
          AND `w_name`.`meta_key` = 'first_name' 
          AND `w_year`.`meta_key` = 'yearofpassing' 
     JOIN `wp_usermeta` as `w_city` ON `w_name`.`user_id`=`w_city`.user_id 
          AND `w_city`.`meta_key` = 'u_city'
     JOIN `wp_usermeta` as `w_course` ON `w_name`.`user_id`=`w_course`.`user_id` 
          AND `w_course`.`meta_key` = 'us_course'
     WHERE 
         `w_name`.`meta_value` = '$us_name' AND         
         `w_year`.meta_value   = '$us_yearselect' AND 
         `w_city`.`meta_value` = '$us_reg' AND 
         `w_course`.`meta_value` = '$us_course'

Other thing: Recommend to use prepared statements, because mysql_* functions is not SQL injection save, and will be deprecated. If you want to change your code the less as possible, you can use mysqli_ functions: http://php.net/manual/en/book.mysqli.php

Recommendation:

Use indexes in this table. user_id highly recommend to be and index, and recommend to be the meta_key AND meta_value too, for faster run of query.

The explain:

If you use AND you 'connect' the conditions for one line. So if you want AND condition for multiple lines, first you must create one line from multiple lines, like this.

Tests: Table Data:

          PRIMARY                 INDEX
      int       varchar(255)    varchar(255)
       /                \           |
  +---------+---------------+-----------+
  | user_id | meta_key      | meta_value|
  +---------+---------------+-----------+
  | 1       | first_name    | Kovge     |
  +---------+---------------+-----------+
  | 1       | yearofpassing | 2012      |
  +---------+---------------+-----------+
  | 1       | u_city        | GaPa      |
  +---------+---------------+-----------+
  | 1       | us_course     | PHP       |
  +---------+---------------+-----------+

The result of Query with $us_name='Kovge' $us_yearselect='2012' $us_reg='GaPa', $us_course='PHP':

 +---------+
 | user_id |
 +---------+
 | 1       |
 +---------+

So it should works.