I am switching jobs. My previous job offered a 401(k) plan and I contributed through payroll. My new company literally offers "no benefits at all" meaning no 401(k), healthcare, etc.
How can I still contribute to my 401(k)?
All this is from CA
You will want to do two things, and do them correctly:
1) You will want to roll over your existing 401K into a Rollover IRA. I would go with either Vanguard or Fidelity. While I have both, I like the website of Fidelity better. You can sign up for free accounts for both and see which one you like better. Some love Vanguard more.
They will help you with the rollover, not charge fees, and give you more investment choices. You want to make sure that you never receive the money, it goes directly from your existing 401(k) to the new one. This avoids a lot of tax hassles.
2) You then want to start your own IRA or Roth IRA. Again, both Vanguard and Fidelity will give great advice on how to get started, what you can contribute, and the mechanics of it all.
Pete's suggestion to roll your money into an IRA is a good way to manage existing money, but you can only contribute an additional $5,500/year (2017 numbers -- $6,500 if you're over 50, but limited in how much you can make and still be eligible to deduct your contributions). $5,500 is much lower than the $18,000 limit for 401(k) contributions.
California is one state that is creating an alternative program that will allow payroll deductions even if you don't have a retirement plan sponsored by your employer. California's plan is called Secure Choice, and they hope to have it available by 2019.
You could also consider moving to a 1099 contract relationship with your employer and pay your own taxes and create a solo 401(k) plan. That assumes your employer would pay you the difference on their share of the payroll taxes and any other benefits that they are currently giving you that you would lose by moving to a contractor relationship.