What you need to do here depends on how you are running your setup, but first of all you need to learn some terminology. There are three basic types of records that nameservers contain about domains and hostnames. These are A MX and CNAME records. An A record resolves a host name e.g. domain.com,
www.domain.com, sub.domain.com etc, to an IP address. An MX record is a Mail eXchange record and resolves mail to a server. A CNAME record is not so straight forward, what it does to to make one hostname inherit all the attributes of another hostname e.g. if you have an A record for domain.com to resolve to 1.2.3.4 and you set an CNAME for example.com to inherit the attributes of domain.com then it will copy domain.com's a record and also resolve to 1.2.3.4. Any chantges to domain.com will also change example.com. In general you should avoid using CNAME records as they tend to be confusing, misunderstood and have consequences that are not forseen. You should stick to A and MX records unless you have hundreds of records to manage.
Back to your situation, I take it that your domain is using the Godaddy nameservers? If it is then you will need to use their control panel to load the records that you need to make all this work. If the domain is not using the Godaddy nameservers then you need to go to the control panel for the people that are running the nameservers for the domain and add the new records in there.
It is perfectly normaly to have your site on one server and have your mail on another. To do this you need to add a couple of A records to resolve your domain and it's most populay subdomain to your server. Assuming your servers's IP is 1.2.3.4 then they should look like:
domain.com A 1.2.3.4
www.domain.com A 1.2.3.4
This resolves your domain and the www subdomain to your webserver.
Now you need to add your MX record. You need to remember that MX records *must* be set to resolve to a hostname and not an IP address. As such you will need to contact Godaddy and find out what the hostnames are that you need to use. For the sake of this let's assume that they are mx1.godaddy.com and mx2.godaddy.com, you then need to add:
domain.com 10 MX mx1.godaddy.com
domain.com 20 MX mx2.godaddy.com
The numbers here are the priority of the records. This means that you mail client will try to use the lower numbered recored first, it if it offline then it will try the next highest one etc.
That should be it. Sorry for the length of this but nameservers records are a rather complicated system that this is barely scratching the surface of.