How I migrated Database from 1.9 to 2.1 (I did mine to a new site with a new database name, you may
have to adjust instructions based on what you are doing)

1. Copy moodle source:
decompress moodle 2.1 files to www/html and copy over to new site

2. mysql stuff:
Let's say your old mysql database name was moodle_learn, and the new one will be m2learn

Run the following line (mysqldump converts your existing moodle_learn database to utf8, then saves it in m2try.sql)

mysqldump -u root -p  -c -e --default-character-set=utf8 --single-transaction --skip-set-charset 
--add-drop-database -B moodle_learn > m2try.sql


vi m2try.sql and do this:
change all references from moodle_learn to m2learn
 

mysql -u root -p  
drop database m2learn  (if it already exists)
create database m2learn charset=utf8;
use m2learn;
SET NAMES 'utf8';
source m2try.sql
quit;

modify the config.php to change the databasename to the new name (i.e. m2learn)

3. Move the moodle data and change chown:
cp -rf /oldsite/moodledata /newsite/moodledata

chown -R moodledata apache:apache
chmod -R 770 on it if necessary

Now just visit the site and it will start walking you thru the upgrade and conversions.

4. I got some errors on things in the database itself - these DDL SQL execution errors and had to make some
patches to the database data.  If you run into that, go here:
http://moodle.org/mod/forum/discuss.php?d=177074#p800423