Router – Connecting two routers via serial

I'm new to Cisco and I wanted to connect two routers with serial connection. This is how my network looks now:

Maybe I connected them wrong because when I try to ping from PC0 to either PC2 or PC3 I get destination host unreachable on the IP of Router0. So I had an idea that there aren't routes between my FastEthernet and Serial ports and I tried to do that but I'm not sure how or if that's even the right approach.

As I said I'm new to this and my knowledge is not large but please if you have any directions, I'd very much appreciate it! Also I'm sorry if I used any wrong terminology since that's also new to me!

EDIT: I forgot, here is some more info on my devices in question:
Router0 has an IP of 192.168.0.1 for Fe0/0 and 192.168.1.1 for Fe0/1 and for Serial 0/1/0 it has an IP of 10.10.10.1. All of them have subnet of 255.255.255.0

Router1 has an IP of 192.168.2.1 for Fe0/0 and 192.168.3.1 for Fe0/1 and also for Serial 0/1/0 it has an IP of 10.10.10.2. Also 255.255.255.0 subnet mask.

My ultimate goal is to be able to ping from PC0 (192.168.0.10) or PC1 (192.168.1.10) to PC2 (192.168.2.10) or PC3 (192.168.3.10) and vice versa!