DOS itself had no networking support. I don't think Windows 3.1 had native networking either - you had to install Novell for LAN networking or Trumpet Winsock to use a modem.
On the DOS side of things, you can configure DOSBox so that one instance acts as an IPX 'server' - a server that other DOSBox clients can connect to in order to form a virtual IPX network over UDP. Programs running under DOS would then be able to use the IPX network - especially useful for games, as back then IPX was typically the only kind of networking available.
DOSBox also has support for emulating modems, tunneling the communication over TCP. It does this by allowing the Hayes dial commands to accept IP address/port combinations corresponding to the DOSBox client on the other end (which would have been set up as a server), which many programs would then just accept without validating them. In the event that a program did validate them and not let you enter anything except numbers, you can still do it by padding the numbers with zeroes. For example, if you wanted to connect to 192.168.1.45:1234, you could 'dial' 1921680010451234. Many modem games can then be played this way without having to use any DOS networking support.