I will assume a client/server architecture although you seem to be suggesting peer to peer. In some cases a per to peer can be as simple as one client running what amounts to an "echo server" but usually at least one client ends up acting as the server however it is implemented so I will generically speak about client/server.
I have found that an important concept of client/server applications is the concept of handling network events much like you handle keyboard and mouse events. In fact if you can wrap them both into a single "event" system you have made your life much easier. In some cases where network latency isn't a huge issue you can send your keyboard and/or mouse input to the server and only handle the network events from the server. This isn't usually practical for very long but it really isn't a bad place to start either. Then you can pick the points where you want to handle local events locally and interpolate between the client and server updates.
Take a MORPG for example where an entity is either moving toward another point on the map (click where you want to go) or not and can be told what its current position is. When an entity is moving, the game loop continues moving the entity along a straight line at a constant rate (distance over time) unless it has reached its destination or is told to stop. The server sends periodic status updates on where it believes the entity should be now and where it is moving to (if at all) to all clients. In cases where the client/server latency is relatively constant the client side movements can seem relatively smooth (even under higher latency) until the latency changes. This introduces hiccups where entities seem to snap back to a position or jump forward in time. This can be mitigated to an extent by tuning the frequency of server updates but it really isn't something the client or server has any control over (assuming internet vs LAN). What we do have some control over is how we handle the discrepancies.
This is where the real pain and trouble comes in as your game will most likely have different requirements than others so there is no one correct solution here. In many cases there is no choice but to snap to a positional update if it is outside of some range that is deemed "unrecoverable". In some scenarios you may be able to increase or decrease the speed of an entity to compensate but this is game specific. Some common implementations have latency ranges where they will freeze clients experiencing latency outside of a range for a period of time or even disconnect them.
This is just a short list of comments within a very narrow minded example but if you have never implemented a multi-user application before it really doesn't hurt to start with broad strokes and fix the details later. This topic can get super murky and mired in details so give something a try and come back when you have some more specific requirements we can offer some hopefully more helpful and usable advice on.