My lab:
Internet - PIX - DMZ - Debian box with two network cards - Intranet

PIX IP: 192.168.0.10
Debian eth0 IP: 192.168.0.11
Debian eth1 IP: 172.19.0.11

The debian box should seperate the internet/dmz from local lan
(intranet). IPtables should work as firewall. All traffic from lan ->
internet should be allowed. All traffic from internet -> lan should be
blocked except established connection opened from lan site.

I have a iptables script, but it seems that I have missconfigured
something. If I try to do a ping a website or a pop3 request to my
internet provider from my machine inside the lan (ip 172.19.l.55), I
get no answer. SSH access to the debian box is working.

Here my script, hopefully that someone can help me to figure out my
mistake. Thanks in advance.

# intranet
IFACE_INT=eth1

# internet
IFACE_EXT=eth0

# loopback
IFACE_LO=lo

# flush filters
iptables -F
iptables -t nat -F

iptables -X
iptables -t nat -X

# policies
iptables -P INPUT DROP
iptables -P FORWARD DROP
iptables -P OUTPUT DROP

# accept ssh
iptables -A INPUT -p tcp --dport 22 -j ACCEPT

# enable ip-Forwarding
echo "1" > /proc/sys/net/ipv4/ip_forward

# *** INPUT ***

# allow all from intranet
iptables -A INPUT -i $IFACE_INT -j ACCEPT

# no internet connection with a local ip!
iptables -A INPUT -i $IFACE_EXT -s 10.0.0.0/8 -j DROP
iptables -A INPUT -i $IFACE_EXT -s 172.16.0.0/16 -j DROP

# allow established internet connection
iptables -A INPUT -i $IFACE_EXT -m state \
--state ESTABLISHED,RELATED -j ACCEPT

# *** FORWARD ***

# intranet -> internet allow all
iptables -A FORWARD -i $IFACE_INT -o $IFACE_EXT -j ACCEPT

# internet -> intranet only if for established connection
iptables -A FORWARD -i $IFACE_EXT -o $IFACE_INT -m state \
--state ESTABLISHED,RELATED -j ACCEPT

# *** OUTPUT ***

# intranet
iptables -A OUTPUT -o $IFACE_INT -j ACCEPT

# loopback
iptables -A OUTPUT -o $IFACE_LO -j ACCEPT

# internet
iptables -A OUTPUT -o $IFACE_EXT -j ACCEPT

# Masquerading
iptables -A POSTROUTING -o $IFACE_EXT -t nat -j MASQUERADE

> iptables -t nat -F

You don't need this. "iptables -F" do what you want.

> # *** INPUT ***
> # no internet connection with a local ip!
> iptables -A INPUT -i $IFACE_EXT -s 10.0.0.0/8 -j DROP
> iptables -A INPUT -i $IFACE_EXT -s 172.16.0.0/16 -j DROP

You forgot "iptables -A INPUT -i $IFACE_EXT -s 192.168.0.0/24 -j DROP"

> # *** FORWARD ***
>
> # intranet -> internet allow all
> iptables -A FORWARD -i $IFACE_INT -o $IFACE_EXT -j ACCEPT

You don't need to do that. Just do:
"iptables -A FORWARD -i $IFACE_INT -j ACCEPT"
The firewall knows that if it have to forward a packet from $IFACE_INT, it
knows that it have to be to $IFACE_EXT

> # internet -> intranet only if for established connection
> iptables -A FORWARD -i $IFACE_EXT -o $IFACE_INT -m state \
> --state ESTABLISHED,RELATED -j ACCEPT

You don't need that. Just need this:
iptables -A FORWARD -m state \
--state ESTABLISHED,RELATED -j ACCEPT

To give your internal hosts permission to ping external hosts, append this
rules:

iptables -A OUTPUT -m state --state NEW -p icmp --icmp-type echo-request -j
ACCEPT
iptables -A FORWARD -m state --state NEW -i $IFACE_INT -p icmp --icmp-type
echo-request -j ACCEPT

I hope this could help.

Nuno Paquete.