You've picked a very difficult thing to do.
Besides the electrical problems, you also have the mechanical problems of making the connector. USB micro connectors are very precisely made, and you are going to have to connect wires to some very fine pins.
I think what you want is beyond what you could reasonably accomplish. I mean you've got like two days of battery time before your phone dies and you lose access to all the information you need to build a charger. You won't be solving all the inherent problems and getting something made quickly enough to do you any good.
I'd suggest you make it a bit easier.
Take a charger with you. The typical wall wart to USB charger you get with your phone.
Now all you have to do is to get enough voltage to it so that it can operate.
"But my charger needs AC," you protest.
Well, it is designed for AC. Most of them will run, though, if you give them enough DC.
Build voltaic cells as described in the other answers here. Stack them to get about half the lowest rating of your power supply, and add stacks in parallel to get more current.
Connect your crude battery to the AC input of the charger. It will then reduce and regulate the voltage to the 5V your phone needs.
Building just that part will also take longer than your phone battery will last without recharging, but the task is simple enough that you can accomplish it without access to the data stored in the phone.
It will take you a good while to accumulate the metal pieces, and build your batteries. You don't have to worry too much about what kind of metal. Pretty much any two metals can be used in a battery - some combinations are better, some will mean you need really tall stacks to get enough voltage together. You just need to be sure you really only have two types of metal in your battery stacks - impure metals can cause you lots of problems.
There's no insulated wire available, so it'll be much easier to attach to the AC prongs on the charger than to the USB pins.
The whole contraption will be dangerous as F. A DC voltage high enough for this trick to work is high enough to be fatal to anyone who manages to touch the (exposed and uninsulated) plus and minus poles of the battery.
Once you have a usable way to charge your phone, you can look into building something better - with the ability to keep your phone operating until that something better is finished - and expect that to take years.
The charger can operate from a lower voltage, but it might not like it. You'll have to weigh getting information from your phone against the chance that your charger will croak the next time you hook it up to the battery.