Also research SEPs.
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Do not research SEP's. They're old school and don't allow you to put away enough money. Basically a solo-401k allows you to put away 15,500 throughout the year based upon your pay that is subject to SE taxes and social security. This is the employee part that you speak of. Then at the end of the year you can put away an additional 25% of your income up to a total of $29,500 of your income as your employer contribution. Total amount is $45,000. You can put this much away if you earn as little as 125k. In order to get that much in a SEP you'd have to earn 225k. Deadline to contribute the Employer portion is your extended due date of your tax return filing.

In order to have a 401k you need to sign a plan document, get a EIN for your trust, and also sign a deferral agreement. You'll have to keep the document up to date but you can pay people to do that. After that it's just a matter of contacting whoever you plan on investing your money with and getting the account application.

Contact a third party administrator to get the documents prepared. Startup costs are about 2k...or you can contact a mutual fund company and they'll do it for much less but you'll have to use their funds and if you leave them you'll have to get a new document anyways. There's a lot more to know but this is the gist...contact that TPA for more detailed info.