I have got a problem. I have seen a lot of people teach how to join another person's world by clicking the "local server multiplayer" button. But I can't find that button in my Minecraft PE 0.13.1 running on my iPhone 6+! There is only a "multiplayer game" button, but not a local server button!
I think I see what you mean. If you are saying that the multiplayer is not working, as worlds on a LAN should appear in the main list but they don't, there is an easy fix. However if you mean how to join an MCPE server on the internet, I've written about that at the bottom.
Joining a server on your local network (WiFi)
You first need to open Minecraft on both devices, turn off multiplayer game in options, open a world, then leave that world again, and turn on multiplayer game in options. This should hopefully reset multiplayer broadcasting, so it should work.
If that doesn't do anything, quit Minecraft on both devices. On your home screen, double tap the home button and end Minecraft by swiping up all the apps (all iOS users probably know this). Then, once again on the home screen swipe up from the bottom of the home screen (from the top if on android) and enable airplane mode on both devices. After ten seconds disable airplane mode, connect to your network and open Minecraft ONLY on the device on which the world is saved on. Wait and other ten seconds and disable airplane mode. Open Minecraft as normal, and you should be able to join.
Joining a server on the internet
However, as I mentioned before, to join a server there is a different method. Open the create world screen as normal, and click on the arrow button in the top right. It is next to to the advanced button.
On this page enter the name you want the server to appear as, followed by the IP, followed by the port number, usually the default.
After this, your server should appear in your worlds list, above the minecraft worlds, there are many servers availible if you have the time to find them (many have websites as well online).
If you two are right by each other, then 1 simply on the hotspot with/without 3g/4g. And the others connect to that hotspot he/she creates, anyone of you host a Lan game, it will work as long as you had set the options for Broadxast to Lan beforehand. That is if you had no routers or had difficulties with it.