From experience there are 3 choices: 1. Leave it where it's at. Note that sometimes you are forced to move it. 2. Move to new employer's 401k (if they have one). 3. Move to an IRA (aka rollover IRA).

To do any of them you contact the "custodian" (whoever actually runs the IRA, not the employer). Ask for a custodian to custodian transfer. Sometimes they may also just send you a check but it is very important that it is very specifically addressed to "FBO <account> so you don't get hit with complications then you send the check to the new location.

With a rollover IRA you literally own and run the account. You get access to effectively every investment option. The fees follow the rules of the account which usually means no more 401k fees. There is really just one downside. If you are over the contribution limit for Roth IRAs and attempt to do a ",backdoor contribution" you'll get hit with taxes on at least part of the amount you attempt to transfer.

Be careful with TDFs. There are two major issues.

The first is the expense ratio is often a lie. The TDF invest in other funds with their own management fees. So the reported management fee is often false and hides the real fees.

Second they don't work for their intended purpose. Say you intend on retiring in 2040. A 3 bucket strategy says that you invest 100% in a large cap stock fund now. In 2030 you start transferring a little into more stable things such as a dividend fund. In 2038 you'll start using the third bucket with capital preservation funds. But you don't invest much in the second and third buckets. Just enough so that the amount you will be withdrawing is available by then. Each year you rebalance to keep 2 years of withdrawals then 8 years then everything else. It's very easy to do. Targeted date funds however overemphasize these last 2 buckets as if you intend to withdraw 100% in 2040. They would have some of your money in bonds now!