Quoting elithar's comment,
You have two options: either turn off Apache (because only one service
can bind to a port), or (better!) use Apache's ProxyPass to proxy any
incoming requests to a specific Hostname to your Go server running on
port (e.g.) 8000. The second method is very popular, robust, and you
can use Apache to handle request logging and SSL for you.
Reverse Proxying
Using Apache on port 80 in this way is called a reverse proxy. It receives all incoming connections on port 80 (and/or port 443 for https) and passes them on, usually unencrypted, via internal localhost connections only, to your Go program running on whatever port you choose. 8000 and 8080 are often used. The traffic between Apache and your server is itself HTTP traffic.
Because your Go program does not run as root, it is unable to alter critical functions on the server. Therefore it gives an extra degree of security, should your program ever contain security flaws, because any attacker would gain only limited access.
FastCGI
You can improve the overall performance of the reverse proxying by not using HTTP for the connection from Apache to the Go server. This is done via the FastCGI protocol, originally developed for shell, Perl and PHP scripts, but working well with Go too. To use this, you have to modify your Go server to listen using the fcgi API. Apache FastCGI is also required. The traffic from Apache to your server uses a more compact format (not HTTP) and this puts less load on each end.
The choice of socket type is also open: instead of the usual TCP sockets, it is possible to use Unix sockets, which reduce the processing load even further. I haven't done this in Go myself, but the API supports the necessary bits (see a related question).
Nginx
Whilst all the above describes using Apache, there are other server products that can provide a reverse proxy too. The most notable is Nginx (Nginx reverse proxy example), which will give you small but useful performance and scalability advantages. If you have this option on your servers, it is worth the effort to learn and deploy.