I have yet to receive my enlistment bonus from the NG. How should I go about getting it?

When you talk to your first line leader you need to have in hand:
1) Your contract stating the specifics of your bonus
2) Documentation that you completed your initial training now qualifying you for payment

With that in hand your chain of command should be able to submit a pay action on your behalf.

Nothing is "automatic".

Have you talked to your Readiness NCO yet?
For your bonus to pay out, your Readiness NCO needs to log into your bonus case in the Guard Incentives Management Program, (GIMS) ensure your contract and bonus addendum are there, check off that you are qualified for payment, then the state incentives manager for TX ARNG has to check off that your are qualified, then the bonus review at Camp Robinson AR as to check off, then NGB, then DFAS as to review and initiate payment. From start to finish these steps can take 4-12 months.
Your Readiness NCO can log into GIMS and see what step your bonus is at right now.
If your RNCO is unwilling to do so, he either failed to initiate it and is embarrassed or worse, does not know how to do that or does not have access to GIMS, in which case you immediately go to your CO and 1SG to have that situation rectified while they also request a BDE Retention NCO or the state incentives manager do your RNCOs job for him.

I know in the Reserves it is not always automatic. We have a packet we sent to finance and the bonus team that verifies the Soldier met their initial obligation (completing training) and the payment begins. Take your paperwork to your S1 or administrative full time support and ask what the process is for bonuses. If they don't know, you can submit a pay inquiry.