If you have a your wifi network card setup with an IP address and it's working (you can ping your host from another machine and vice versa)
you have your ethernet card setup with an IP address. (I am gonna assume that this card is connected somehow to the internet) and you can ping some address out in the ether.
Then all you need to do is turn on "IP FORWARDING"
By default - most modern Linux's have IP forwarding turned off.
You can check by
if the result is 0 (zero) - then it's off.
To turn it on temporarily ...
echo 1 > /proc/sys/net/ipv4/ip_forward
Now packets from the wifi should be able to flow through your host and out to the internet.
If you are using ipv6 then you should search for the (different) details with regard to ipv6 forwarding.
Of course - you will also need to adjust your routing tables on the client. To say "my default route (gateway) for stuff is that machine over there".
I apologise if it appears that I haven't given the "complete solution on a plate" - but, I am assuming you wanted "pointers in the right direction".