How do I set ufw to allow internal network connections?

I'm configuring an Ubuntu Server for my home network to handle NAT and firewall. I've configured dnsmasq and verified that it's working correctly. I want all connections from my internal network to be allowed. However, once I enable ufw, the connections are blocked.

I have tried:

sudo ufw allow in on eth1

and:

sudo ufw allow from 192.168.0.0/24

but any solution I try results in messages such as these in syslog:

[UFW BLOCK] IN=eth1 OUT=eth0 SRC=192.168.0.10 DST=91.189.94.156 LEN=60 TOS=0x00 PREC=0x00 TTL=63 ID=16240 DF PROTO=TCP SPT=37444 DPT=80 WINDOW=5840 RES=0x00 SYN URGP=0

Am I understanding the rules incorrectly, or is the problem elsewhere?

It looks like you may have "default deny outgoing" turned on. Can you do a "sudo ufw status verbose" for us please? I'm assuming that you're server IP address is not 91.189.94.156. Are you using your server as a gateway? If so, check out this link, which shows hot to set it up (or close to what you need).