Requirements:
phpMyAdmin on both servers (unless you know what you mean with servers)
very good FTP cleint (I suggest Flash FXP)
very good text editor (I suggest UltraEdit-32)
patience
a little bit of knowledge of how 4images works
Can we sum the steps as:
1) Back Up the database as
.sql or .zip [Old Server]
*.sql recommended2) Back Up the /4images directory entirely [Old Server]
3) Restore the database [New Server]
1 *see below4) Note down the database information (domain, user, database, etc.) [New Server]
5) Restore /4images directory [New Server]
6) Edit config.php and other .phps under /4images to match the new domain, user, database, etc [New Server]
2 *see belowIf you are making a dummy duplicate of 4images, above should work, because all the prefix and subfolders & data should match each other.
Only problem could be if there is a mod which needs to link to db and you forgot to rename/modify & give it the new db specs.
1) While restoring database, you may runinto problems during importing or while restoring the db.sql into your new db. This can cause time out and 50x errors with your server. To avoid this try restoring 4images_ tables one at a time. Try exporting 1 table, and importing 1 table, and so on.. such as start with 4images_categories and export it, later 4images_comments.. and so on. You may run into problem with tables that are over 750kb, depending on your connection and the speed of your server. What to do? Then as v@no suggested try opening the .sql file and use SQL to run SQL query/queries on database. 4images_wordmatch can cause a problem, because on mine it was 1.7MB, which consists of simple commands like
INSERT INTO 4images_wordmatch VALUES (1, 41, 0, 0, 1);
INSERT INTO 4images_wordmatch VALUES (1, 40, 0, 0, 1);
INSERT INTO 4images_wordmatch VALUES (1, 39, 0, 0, 1);
INSERT INTO 4images_wordmatch VALUES (1, 38, 0, 0, 1);
INSERT INTO 4images_wordmatch VALUES (1, 37, 0, 0, 1);
INSERT INTO 4images_wordmatch VALUES (1, 36, 0, 1, 0);
INSERT INTO 4images_wordmatch VALUES (1, 35, 0, 1, 0);so it is pretty easy to input line by line, try doing 750 lines at a time.
2) There are only 3-5 files which needs to link to db, if you think you might have more, you will use your favorite search tool to search for file "Containing Text = xxxxx (your db or your db password)" and the result files needs to be modified to your new db information. The best text editor I found is UltraEdit-32 which can find and replace any given words in all open files at once.
Keep reading for other updates and details.
Good Luck. 
