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Make sure PLEX has a normal IP address.  So in the router, you would assign the device PLEX is on with a Static IP address.  For example, my PLEX server is on my NAS.  My NAS has a static IP number of 10.0.0.100.  It never changes.  Because otherwise DHCP on your router will Auto assign IP numbers on your local Network to anything in it's range.  Yo may be on 192.168.0.1 though 192.168.0.255.  I'm on the 10.0.x.x Network.  These are IP address reserved for use for interal networks. There's a few others also.  192.168.x.x. is problebly the most common.  

So every device that has a Network connection, WIRED or WIRELESS has a MAC address. If it has both, it has one for each.  There's not the same.  Every device has it's own MAC address.  Even if you have 2 of the same of anything, the MAC address is going to be differnt.   There's a number of ways to get the MAC address.    But you'll want to go into your router settings and Lock a IP address to the MAC address of the device.  The MAC address would look something like 34:13:AZ:4E:76:32.   This is a pretty basic thing to do.  I have most of my network stuff locked to a Static IP number.  It makes for a more reliable network.    On my ASUS TM-AC1900 (This was a nice free Router from T-Mobile) You would click on LAN on the left then click on DHCP server on the top.  Then if you scroll down you see "Manually Assigned IP around the DHCP list (Max Limit : 64)"

So the left colume it shows MAC Address.  You can scroll though the devices it currently see's ir enter the MAC address like I have it above in that format.   The next colume is IP address.  So pick a IP address for that's in the range of IP address your router is setup for.  If you're using 192.168.1.1 for your router, You could do something like 192.168.1.10.  The Next colume there's a Add/Delete.  You want to click on the Plus to Add.  Then on the bottom of the Page you want to click on Apply.   You've now locked your PC or NAS or whatever to that IP address.  You can do this with any router.  How exacly depends on the router you have.

Once that is done, This is when you want to Port Forward.  See if you were forwarding a port to where your device currently is from what DHCP assigned to it, and then it changes later, the port could be forwarding to some other device or nothing at all.  This is why you want to lock down the device to a IP number that never changes.

So to port forward.  What IP number is your PLEX Server using?  If you go into PLEX then click on server and then on the left Remote Access,  You want to click on the Box for "Manually specify public port",  I'm using a port number of 32400.  If you have nothing there, g use that number and hit apply.

Back in my Router on the left, I want to now click on the WAN box.  Then on top there's "Virtual Server / Port Forwarding"  Click on that.  You scroll down and you get "Port Forwarding List (Max Limit : 32)"  You have more columns.  First one is "Service Name"  That's easy just put PLEX.  That way you know what that port forward is for.  The Next Column is port range.  So enter 32400 or whatever YOU are using.  The next Column is Local IP.  So you would put 192.168.1.10 or whatever your PLEX server is running on that you created a Static IP number for above.  Next Column is Local Port.  Again put 32400 or whatever port you're using.  The last Column is "Protical"  SO it's either TCP, UPD or BOTH.  In general unless you're 100% sure, just put BOTH. It' not going to hurt things.

So if PLEX is working connecting correctly, it should look like this.

So if you look Right to left, you start at INTERNET, with a Green arrow going to my current IP address MY ISP game me with the port number, that's Public, with another green arrow, to my Private Network of 10.0.0.100:34200   That's showing that I have a good outside network connection.  You also need to have PLEX linked to PLEX service, Up top on the right.  So if you go into account, at top for me it shows Plex Pass  as I'm a lifetime member.  You should be all logged IN.  This allows your server to send info to PLEX of what your current IP address your ISP gave you.  So if you load up PLEX on your iPhone for example, and logged into your account, PLEX will know what your current IP number.  So you'll be sent to your IP number your IPS gave you, using the port number you assigned to get onto your server.

Doing port forwarding is something that you need to really do if you do Online gaming, or you Torrent and want it to work correctly, you want to forward the needed port. For example the port I use for UTorrent is 50722.  SP you would do the same thing you did for PLEX.  For whatever you have UTorrent running on.  You can find the port UTorrent is using in the settings.   

So I can star t PLEX onmy iPhone, I'm all setup on my phone, do i just lick on Music and then I cna browse around, basically get around just like I would if I was on my computer.  I can pick what I want to play and it plays.  it's really SIMPLE!!! Or I can play a movie, or view a picture.  Though I would do those things while driving a car.  It ALL works just like if you were using PLEX on your computer.  I have a Friend account setup for friend of mine and she can log onto my PLEX whenever she likes and watch something or play the music. Whatever I give her account access to.  She watches on your HDTV using a ROKU.   I can go to my brothers house and Airplay onto his AppleTV.  Theses are the things you cna do with PLEX.  You can go anywhere in the world with a Internet connection and get onto PLEX at home EASY!!!   I stream video at work all the time when I'm on my lunch break,   I put on my Bluetooth Headphones and play Plex on my iPad at work.  Works great and I connect easily.  I don't have to know what my home IP number is.  That's taken care of automatically.

No fixed IP address is needed!!!  Few Home Users have a fixed IP address.  There are services that you can use for other things if you have a IP address that's always changing.    Again, Yes, Using my iPhone to get my PLEX Music in my Car.  It'll work the same way with Android.  There's a App!!!