How to create relationships in MySQL

If the tables are innodb you can create it like this:

CREATE TABLE accounts(
    account_id INT NOT NULL AUTO_INCREMENT,
    customer_id INT( 4 ) NOT NULL ,
    account_type ENUM( 'savings', 'credit' ) NOT NULL,
    balance FLOAT( 9 ) NOT NULL,
    PRIMARY KEY ( account_id ), 
    FOREIGN KEY (customer_id) REFERENCES customers(customer_id) 
) ENGINE=INNODB;

You have to specify that the tables are innodb because myisam engine doesn't support foreign key. Look here for more info.

CREATE TABLE accounts(
    account_id INT NOT NULL AUTO_INCREMENT,
    customer_id INT( 4 ) NOT NULL ,
    account_type ENUM( 'savings', 'credit' ) NOT NULL,
    balance FLOAT( 9 ) NOT NULL,
    PRIMARY KEY ( account_id )
)

and

CREATE TABLE customers(
    customer_id INT NOT NULL AUTO_INCREMENT,
    name VARCHAR(20) NOT NULL,
    address VARCHAR(20) NOT NULL,
    city VARCHAR(20) NOT NULL,
    state VARCHAR(20) NOT NULL,
)

How do I create a 'relationship' between the two tables? I want each account to be 'assigned' one customer_id (to indicate who owns it).

You have to ask yourself is this a 1 to 1 relationship or a 1 out of many relationship. That is, does every account have a customer and every customer have an account. Or will there be customers without accounts. Your question implies the latter.

If you want to have a strict 1 to 1 relationship, just merge the two tables.

CREATE TABLE customers(
    customer_id INT NOT NULL AUTO_INCREMENT,
    name VARCHAR(20) NOT NULL,
    address VARCHAR(20) NOT NULL,
    city VARCHAR(20) NOT NULL,
    state VARCHAR(20) NOT NULL,
    account_type ENUM( 'savings', 'credit' ) NOT NULL,
    balance FLOAT( 9 ) NOT NULL,
)

In the other case, the correct way to create a relationship between two tables is to create a relationship table.

CREATE TABLE customersaccounts(
    customer_id INT NOT NULL,
    account_id INT NOT NULL,
    PRIMARY KEY (customer_id, account_id),
    FOREIGN KEY customer_id references customers (customer_id) on delete cascade,
    FOREIGN KEY account_id  references accounts  (account_id) on delete cascade
}

Then if you have a customer_id and want the account info, you join on customersaccounts and accounts:

SELECT a.*
    FROM customersaccounts ca
        INNER JOIN accounts a ca.account_id=a.account_id
            AND ca.customer_id=mycustomerid;

Because of indexing this will be blindingly quick.

You could also create a VIEW which gives you the effect of the combined customersaccounts table while keeping them separate

CREATE VIEW customeraccounts AS 
    SELECT a.*, c.* FROM customersaccounts ca
        INNER JOIN accounts a ON ca.account_id=a.account_id
        INNER JOIN customers c ON ca.customer_id=c.customer_id;

as ehogue said, put this in your CREATE TABLE

FOREIGN KEY (customer_id) REFERENCES customers(customer_id) 

alternatively, if you already have the table created, use an ALTER TABLE command:

ALTER TABLE `accounts`
  ADD CONSTRAINT `FK_myKey` FOREIGN KEY (`customer_id`) REFERENCES `customers` (`customer_id`) ON DELETE CASCADE ON UPDATE CASCADE;

One good way to start learning these commands is using the MySQL GUI Tools, which give you a more "visual" interface for working with your database. The real benefit to that (over Access's method), is that after designing your table via the GUI, it shows you the SQL it's going to run, and hence you can learn from that.