Can you provide more information on how to check if the Docker daemon is running correctly? with example

Check the Docker service status

# systemctl status docker
   docker.service - Docker Application Container Engine
   Loaded: loaded (/usr/lib/systemd/system/docker.service; enabled; vendor preset: disabled) 
   Active: active (running) since Mon 2023-02-06 12:41:23 UTC; 3h 57min ago
   Main PID: 745 (dockerd)
   Status: "Docker is up, running and healthy on this host."

Check The Docker process

# ps aux | grep docker
root      745  0.5  0.8 135512 15624 ?        Ssl  12:41   0:03 /usr/bin/dockerd -H fd:// --containerd=/run/containerd/containerd.sock

Check The Docker version

# docker version
	Client: Docker Engine - Community
	Version:           20.10.17
	API version:       1.41
	Go version:        go1.16.15
	Git commit:       ag90e39
	Built:             Mon Feb 6 18:49:38 2023
	OS/Arch:           linux/amd64
	Context:           default
	Experimental:      true

Server: Docker Engine - Community 
 Engine:
  Version:          20.10.17
  API version:      1.41 (minimum version 1.12)
  Go version:       go1.16.15
  Git commit:       ag90e39
  Built:            Mon Feb 6 18:49:31 2023
  OS/Arch:          linux/amd64
  Experimental:     false
 containerd:
  Version:          1.6.6
  GitCommit:        847e7252d6968d164259782487e11fd5467ddf55
 runc:
  Version:          1.2.1
  GitCommit:        bdb5fbc29303ca190e782297e76c28bac8f0d7c1

Pull the test image to verify

# docker pull hello-world

Run test container
# docker run hello-world
Hello from Docker!