If you happen to use CentOS 8 you have already discovered that Red Hat (i.e. CentOS) switch to podman, which is a fork of docker. So probably the following fix might help to someone, which does not use CentOS 8 or podman. For now, podman and docker are 99.99% the same.
So creating and starting a container is easy and in most cases one command only, but you may stumble on the error your container could not resolve or could not connect to an IP even there is a ping to the IP!
The service in the container may live a happy life without Internet access but just the mapped ports from the outside world. Still, it may happen to need Internet access, let’s say if an update should be performed.
Here is how to fix podman (docker) missing the Internet access in the container:

• No ping to the outside world. The chances you are missing

  sysctl -w net.ipv4.ip_forward=1
  

  And do not forget to make it permanent by adding the “net.ipv4.ip_forward=1” to /etc/sysctl.conf (or a file “.conf” in /etc/sysctl.d/).

• ping to the outside IP of the container is available, but no connection to any service is available! Probably the NAT is not enabled in your podman docker configuration. In the case with firewalld, at least, you must enable the masquerade option of the public zone

  firewall-cmd --zone=public --add-masquerade
  firewall-cmd --permanent --zone=public --add-masquerade
  

  The second command with “–permanent” is to make the option permanent over reboots.

The error – Could not resolve host (Name or service not known) despite having servers in /etc/resolv.conf and ping to them!

One may think having IPs in /etc/resolv.conf and ping to them in the container should give the container access to the Internet. But the following error occurs:

[root@srv /]# yum install telnet
Loaded plugins: fastestmirror, ovl
Determining fastest mirrors
 * base: artfiles.org
 * extras: centos.mirror.net-d-sign.de
 * updates: centos.bio.lmu.de
http://mirror.fra10.de.leaseweb.net/centos/7.7.1908/os/x86_64/repodata/repomd.xml: [Errno 14] curl#6 - "Could not resolve host: mirror.fra10.de.leaseweb.net; Unknown error"
Trying other mirror.
http://artfiles.org/centos.org/7.7.1908/os/x86_64/repodata/repomd.xml: [Errno 14] curl#6 - "Could not resolve host: artfiles.org; Unknown error"
Trying other mirror.
^C

Exiting on user cancel
[root@srv /]# ^C
[root@srv /]# ping 8.8.8.8
PING 8.8.8.8 (8.8.8.8) 56(84) bytes of data.
64 bytes from 8.8.8.8: icmp_seq=1 ttl=56 time=5.05 ms
64 bytes from 8.8.8.8: icmp_seq=2 ttl=56 time=5.06 ms
^C
--- 8.8.8.8 ping statistics ---
2 packets transmitted, 2 received, 0% packet loss, time 1000ms
rtt min/avg/max/mdev = 5.050/5.055/5.061/0.071 ms
[root@srv ~]# cat /etc/resolv.conf 
nameserver 8.8.8.8
nameserver 8.8.4.4
[root@srv /]# ping google.com
ping: google.com: Name or service not known

The error 2 – Can’t connect to despite having ping to the IP!

[root@srv /]# ping 2.2.2.2
PING 2.2.2.2 (2.2.2.2) 56(84) bytes of data.
64 bytes from 2.2.2.2: icmp_seq=1 ttl=56 time=9.15 ms
64 bytes from 2.2.2.2: icmp_seq=2 ttl=56 time=9.16 ms
^C
[root@srv2 /]# mysql -h2.2.2.2 -uroot -p
Enter password: 
ERROR 2003 (HY000): Can't connect to MySQL server on '2.2.2.2' (113)
[root@srv2 /]#

Despite having ping the MySQL server on 2.2.2.2 and despite the firewall on 2.2.2.2 allows outside connections the container could not connect to it. And testing other services like HTTP, HTTPS, FTP and so on resulted in “unable to connect“, too. Simply because the NAT (aka masquerade is not enabled in the firewall).