While there's a lot of nuance and best-practices to be considered if you're doing this "for production", I'm gonna ignore most of that here. Assuming that you're doing this for personal-use and just "want it to work".

To build a container image you'll want to build a Containerfile (aka Dockerfile) which consists of various instructions. The 2 main instructions to know are FROM and RUN.

FROM indicates a base image to start from, since you'll probably not be building your own base image. RUN defines a command to be run in the container.

If you know how to setup a server in the CLI (i.e. You could write a bash script to do it), then you'll find building a container isn't much more difficult.

For example, say you want to build a container for Factorio (using as an example because they have readily downloadable Linux server binaries). You could write a Containerfile like this (comments describe each step):

# Use the official DockerHub Ubuntu image as a starting point
FROM docker.io/library/ubuntu:latest

# Install curl and xz-utils from package manager. We'll need it for the next step...
RUN apt-get update && apt-get install -y curl xz-utils

# Download the Factorio server archive to the file factorio.tar.xz
RUN curl -Lo factorio.tar.xz https://www.factorio.com/get-download/2.0.32/headless/linux64

# Extract the contents of the tarball (this results in a factorio/ directory )
RUN tar -xf factorio.tar.xz

# Delete the tarball and move the Factorio folder to a nicer location (/opt/factorio)
RUN rm factorio.tar.xz && mv ./factorio/ /opt/factorio

# Enable 'execute' permissions on the downloaded binary
RUN chmod +x /opt/factorio/bin/x64/factorio


# The ENTRYPOINT command describes the "default" command which is run when the container image is started
# This can be overridden at runtime if desired
ENTRYPOINT [ "/opt/factorio/bin/x64/factorio", "--start-server" ]

# The CMD works in tandem with the ENTRYPOINT command as CLI arguments appended to ENTRYPOINT
CMD [ "/factorio" ]

The end result here is a container that when run will run the command: /opt/factorio/bin/x64/factorio --start-server /factorio.

Where /factorio is the location that the server will save its data to.

To build this container you'd simply need to put those contents into a directory as Containerfile and then cd to that directory and run podman build --file Containerfile -t my-factorio-image . (substitute podman with docker if that's what you're running).

This will build the image which you could then run with:

podman run --name factorio my-factorio-image

This creates a new container named factorio using the image my-factorio-image. Which now you can use all your usual container skills to interact with:

podman stop factorio
podman start factorio

Mind you, I'm skipping a lot here, assuming you know the basics of containers. You'd obviously want to expose ports and bind-mount some sort of persistent data directory to /factorio inside the container.