The easiest way I have found is to dump the database to a text file, run a sed command to do the replace, and reload the database back into MySQL.

All commands are bash on Linux, from memory.

Dump database to text file

mysqldump -u user -p databasename > ./db.sql

Run sed command to find/replace target string

sed -i 's/oldString/newString/g' ./db.sql

Reload the database into MySQL

mysql -u user -p databasename < ./db.sql

Easy peasy.

Put this in a php file and run it and it should do what you want it to do.

// Connect to your MySQL database.
$hostname = "localhost";
$username = "db_username";
$password = "db_password";
$database = "db_name";

mysql_connect($hostname, $username, $password);

// The find and replace strings.
$find = "find_this_text";
$replace = "replace_with_this_text";

$loop = mysql_query("
 SELECT
 concat('UPDATE ',table_schema,'.',table_name, ' SET ',column_name, '=replace(',column_name,', ''$find'', ''$replace'');') AS s
 FROM
 information_schema.columns
 WHERE
 table_schema = '$database'")
or die ('Cant loop through dbfields: ' . mysql_error());

while ($query = mysql_fetch_assoc($loop))

 mysql_query($query['s']);

Running an SQL query in PHPmyadmin to find and replace text in all wordpress blog posts, such as finding mysite.com/wordpress and replacing that with mysite.com/news
Table in this example is tj_posts

UPDATE `tj_posts`
SET `post_content` = replace(post_content, 'mysite.com/wordpress', 'mysite.com/news')

 UPDATE table SET field = replace(field, text_needs_to_be_replaced, text_required);

Like for example, if I want to replace all occurrences of John by Mark I will use below,

UPDATE student SET student_name = replace(student_name, 'John', 'Mark');

Another option is to generate the statements for each column in the database:

SELECT CONCAT(
 'update ', table_name , 
 ' set ', column_name, ' = replace(', column_name,', ''www.oldDomain.com'', ''www.newDomain.com'');'
) AS statement
FROM information_schema.columns
WHERE table_schema = 'mySchema' AND table_name LIKE 'yourPrefix_%';

This should generate a list of update statements that you can then execute.

I believe "swapnesh" answer to be the best ! Unfortunately I couldn't execute it in phpMyAdmin (4.5.0.2) who although illogical (and tried several things) it kept saying that a new statement was found and that no delimiter was found…

Thus I came with the following solution that might be usefull if you exeprience the same issue and have no other access to the database than PMA…

UPDATE `wp_posts` AS `toUpdate`,
(SELECT `ID`,REPLACE(`guid`,'http://old.tld','http://new.tld') AS `guid` 
 FROM `wp_posts` WHERE `guid` LIKE 'http://old.tld%') AS `updated`
SET `toUpdate`.`guid`=`updated`.`guid`
WHERE `toUpdate`.`ID`=`updated`.`ID`;

To test the expected result you may want to use :

SELECT `toUpdate`.`guid` AS `old guid`,`updated`.`guid` AS `new guid`
FROM `wp_posts` AS `toUpdate`,
(SELECT `ID`,REPLACE(`guid`,'http://old.tld','http://new.tld') AS `guid`
 FROM `wp_posts` WHERE `guid` LIKE 'http://old.tld%') AS `updated`
WHERE `toUpdate`.`ID`=`updated`.`ID`;

Generate change SQL queries (FAST)

mysql -e "SELECT CONCAT( 'update ', table_name , ' set ', column_name, ' = replace(', column_name,', ''www.oldsite.com'', ''www.newsite.com'');' ) AS statement FROM information_schema.columns WHERE table_name LIKE 'wp_%'" -u root -p your_db_name_here > upgrade_script.sql

Remove any garbage at the start of the file. I had some.

nano upgrade_script.sql

Run generated script with --force options to skip errors. (SLOW - grab a coffee if big DB)

mysql -u root -p your_db_name_here --force < upgrade_script.sql

the best you export it as sql file and open it with editor such as visual studio code and find and repalace your words.
i replace in 1 gig file sql in 1 minutes for 16 word that total is 14600 word.
its the best way.
and after replace it save and import it again.
do not forget compress it with zip for import.