Once you click the link for phpMySQL, it will probably open a new window. There are two frames that make up this page, a skinny one on the left and a larger frame on the right. On the left is a drop down box labeled "Database". No matter how many you have, use the drop down box to select the data base. It should flicker and eventually open a list of what tables are in the database. When the list of tables appears on the left another window will open on the right, if the window on the right doesn't also reload and show a list of the tables, you'll need to click on the name of the database above the list of tables on the left to load the list on the right. Sounds confusing, I know, but do it just like that and it works.

Next, above the table on the top right, there are tabs labeled Structure, SQL, etc... Choose the one labeled "Export". When the next window loads, it should have a list of your tables in a scrolling box. In my version of phpMyAdmin it's in the top left corner of the right side frame. It has a link labeled "Select All", click it, it should highlight the list or show you it has selected them somehow. Generally speaking, doing this creates an SQL file by default so all the other settings are for advanced users. Find the "Go" button. Click that.

The page that loads make take a minute or two depending on how big your database is or how fast the host is. What comes out is the database in text format, SQL format. In the text box, right click and select all, copy the text and open a text editor. A simple one is best. WordPad does good because it doesn't alter the test and has a "Replace All" feature. Paste The Data text into the editor.

TIP: When you move to the new server, create a database as closely to the configuration to the original as possible so you don't have to change any configuration files in your website programs, forums or CMS using the SQL database.

Modifying SQL Database To New Server
Find the location of an old server path in the text, using the find feature for your username is usually the easiest and most common way web hosts create hosting accounts. Once you locate the old server path, do what ever your text editor requires to replace this text. In WordPad, you highlight the text to be replaced, go to the "Edit" tab and select "Replace All". It automatically has the text to be replaced and you only need to enter the new server path in the lower window. Once there, click "Replace All" and that's about it. Save the file as a plain text (.txt) file but name it with the .sql extension, type the whole thing in as the filename and it will make it that type of file.

If you are moving to or using a copy for a new domain name, you may need to replace those in the data file also.

I always like to double check my paths and use the find feature to hunt out any instances of an old path, but usually they are all knocked out the first time you replace it.

Lastly, the easy part, uploading the new version of the database to the new host...and you have two options.
YOU SHOULD HAVE ALREADY CREATED A NEW DATABASE TO FILL.
The First method, the one I use most is to go into the phpMyAdmin like before, select the tab "SQL" on the top, then it opens a window with a large text area. I paste a copy of the new version into this then hit "GO". This runs the commands and loads the information from the file. It takes a while to load sometimes so be patient. Once it's done, it will confirm or show errors. Also, the frame on the left should reload with all the tables you just added. If it doesn't, click the drop down box and choose the database again and see if it loads up then.
The second way is to select "Import". From this screen, there should be a "Browse" button next to a text box. It looks like a search box, but it let's you look into your files and select the SQL database text file you created. Select it, Click "Open", then find the nearest "Go" button. This method will take just as long as the other, but can time out on some hosts if it is too large. As in the first example, once the information is loaded, the new tables should be showing on the left and maybe on the right.

If your server times out or get errors because the text file or data you pasted at the new server is too large, you'll need to use the first method from above. Go into the new text file and grab sections of the database information to load at a time. Usually, splitting it in half, or close to it, should solve the problem. It's obvious how you should grab the information to paste, it's clearly marked where the table information begins and ends, just select text up to a break between tables and copy that, then the other half.

If the versions of phpMyAdmin are too different, you may need to go back to the first step of getting a copy of the data base and finind a selection that makes a copy compatible to your version.

Keep It Str8!