MS SQL Express is a free database server for learning and building small web and desktop applications. Here you will be guided on how to perform a new SQL Server 2019 Express Edition installation on a Windows 10. Follow these simple steps.
1. Download 'SQL Server Installer for Express Editions'
Download URL https://www.microsoft.com/en-gb/download/details.aspx?id=101064
The name of the installation file is 'SQL2019-SSEI-Expr.exe', size 6.231Mb
2. Run 'SQL2019-SSEI-Expr.exe' - Installation Type

If you wish to configure which components should be installed then choose 'Custom'. The 'Basic' installation type installs SQL Server Database with the default configuration. In our example, I choose 'Custom'.
3. Target Location for installation files

By default use 'C:\SQL2019'.
4. Downloading install package

5. SQL Server Installation Center

6. License Terms

7. Install Rules

8. Feature Selection

If you don't plan to use 'SQL Server Replication' or 'Machine Learning Services and Language Extensions' feel free to uncheck these features. But I did not uncheck them. Perhaps I may use it at least for learning purposes. The only thing you should specify - CAB files for machine learning in one of the next steps.
9. Instance Configuration

Set the name of your SQL Server Instance. You will use this name to connect the SQL server.
10. Java Install Location

Open JRE 11.0.3 is required for some features we chose in step 8.
11. Server Configuration

The main purpose of this step is to configure 'Startup Type'. By default use the 'Automatic' at least for the SQL Server Database Engine.
12. Server Configuration - Collation
Collation. In my case it is Ukrainian, but if you are from an English-speaking country like the US select the 'Latin1_General'.
13. Database Configuration Engine

Select Mixed Mode. It allows use SQL Server authentication(user and password) and Windows authentication(current user).
14. Data Directories

Use default data directories provided by installation manager.
15. TempDB - Database Engine Configuration

User default TempDB configuration.
16. Memory configuration

Database Engine Configuration - Default Memory configuration.
17. User Instances

'User are allowed to run a separate instance of the Database Engine' checked by default.
18. Filestream

Default configuration.
19. Consent to install Microsoft R Open

20. Consent to install Python

21. Microsoft Machine Learning Server Components

During this step, I faced the problem that the installation manager was not being able to contact with download center. Using the links under the 'Install Path' I manually downloaded the CAB files:

22. Installation Progress

23. Installation Complete

24. Run SQL Server 2019 Configuration Manager

25. SQL Server 2019 Configuration Manager
You may also be interested in how to test connection to your SQL server.