How to connect ESP8266 12e directly to Arduino Uno (without shields)
Make sure to specify as SoftwareSerial's Rx pin, the pin# connected to the ESP's Tx pin. They have to be crossed. (I just fumbled that myself, a couple of hours ago ):

It is the ESP's Rx pin that needs the voltage divider.

Also pullup the ESP's reset pin.

Update:

ESP-01 and ESP-12 modules use the same ESP8266 chip. The differences are in the number of pins brought out from the chip and made available on the board. Other differences include the firmware interpreters installed on them before shipment: "NodeMCU" is one. ESP-01 is usually shipped with the AT+ command interpreter unless it specified otherwise; I would expect the same for the others. Bottom line is they are connected pretty much alike. Interacting with them serially from an Arduino (or other device) then depends on the installed firmware, including whether you've installed your own. So far, I've used all of mine as WiFi modules using the AT+ interpreter they came with.


  How can I pullup the reset pin? Also do I need to pullup it just for
  initial setup (changing baud rate and such) or should it be pulled up
  at all times?


I use a 10K-Ohm resistor to +3.3v as a pullup. You need it pulled up anytime you are not trying to force a hardware reset; grounding it resets the chip. I have never used a reset button on my ESPs. I just leave them pulled up. If you want one, it should short the reset pin to ground.

Update 2 (wiring):

You've powered the ESP with 3v but your pullups are taken to the Arduino's 3.3v supply. Most chips have a slim tolerance for signal levels above their supply voltage. I'd suggest driving the entire ESP from your 3v battery - power &amp; both pullups.

I don't know the ESP-12E's pinouts to check them; I'm sure you have, and you might want to label the diagram so someone else can look over it too.

Then there's whatever "chicken dance" is needed on the reset and the GPIO line that needs to get toggled to start an upload. I don't know that sequence, but I think you need a grounding buttons on on each one to be able to sequence them.