Make sure your players are on board.
Before even going down this path, you may wish to make sure your players are on board with it. If your players are showing up expecting to solve most problems through combat, they may not even look at other options. They may well suspect that you don't want them to look at other options, and indeed many role playing games deliberately center tactical combat and exploration with just enough social interaction to provide a reason for the combat and exploration. Many players and many gms want that.
And along those lines, you need to make sure that your players are at least willing to try a more diplomatically focused game and preferably that they want it. If you try to force diplomacy and negotiation on a group that wants combat, you may wind up with unhappy players.
Use a system that encourages such things.
Role playing games are versatile. You can make just about any role playing system do just about anything you want. But, different systems support different subsets of rules to differing degrees and your choice of system may make some types of games easier or harder.
D&D stereotypically focuses mostly on combat. Its combat system is superbly developed. Historically, it grew out of and was influenced by pure war games such as chainmail. Due to things like Stranger Things, the popular conception of it centers on fighting. While you certainly can do diplomacy in D&D (and I have), it is in my opinion not the best system for it and unless expressly told otherwise I think most players showing up to a D&D game expect exploration and combat.
On the other hand, there are other games that are much more suited to intrigue. Vampire The Masquerade for instance has more developed rules and systems around intrigue, negotiation, and diplomacy. I have gone for entire sessions without even the threat of combat. Other systems like Exalted have both deep developed social influence systems and deep combat systems.
To be clear, you can play a game with diplomacy and negotiation in just about any mainstream system, but if you want to highlight those things, you may find it easier to do it in some systems than others.
Provide situations where diplomacy is clearly the superior option.
Finally, and this is related to Dale M's answer, if you want to encourage diplomacy and negotiation, provide situations where that is clearly superior.
One of the obvious ways is to provide situations where someone that is normally an ally is an obstacle, preferably in a way that is reasonable. Imagine that the ally has a MacGuffin that the players want or even need. The players should be reluctant to take it by force because doing so would require attacking an ally. The ally likely has a legitimate reason to be reluctant to give up the MacGuffin. But the players may be able to negotiate to get it, providing something else the ally wants more or at least persuading the ally that it is imperative to give it up.
Also, and this is somewhat system dependent, but as Dale M suggests make sure there are clear rewards for succeeding in the negotiation. In D&D and similar systems, make sure the players remember that experience is issued for overcoming obstacles even if, and sometimes especially if its done non-violently.
While its older, the Planescape Torment CRPG provides examples of a game that I think handles it well. The vast majority of combat can be avoided if you want, and often the best results (including experience points and levels) come from socially resolving problems rather than fighting.