simplest possible script for backing up your DB with sh + cron

backuper.sh

#!/bin/bash

# usage:
# crontab -e
# 20 1 * * * /bin/bash /home/user/bin/backuper.sh

## configuration {
BACKUP_DIR="ABSOLUTE_PATH_TO_BACKUP_DIR"
DBNAME="UR_DB_NAME"
DBUSER="UR_DB_USER"
DBPASSWD="UR_DB_PASSWORD"
DATE_TEMPLATE="$(date '+%Y.%m.%d')"
DAYS_TO_STORE=30
## }

fname="${BACKUP_DIR}/${DBNAME}_${DATE_TEMPLATE}.sql"

# ensure existence of $BACKUP_DIR
mkdir -p "$BACKUP_DIR"

mysqldump --user="$DBUSER" --password="$DBPASSWD" "$DBNAME" > "$fname"
gzip --best "$fname"

# delete old backups
find "$BACKUP_DIR" -type f -name "*.gz" -ctime "$DAYS_TO_STORE" -delete