Shot in the dark

I just bought this on the assumption it is small approx 1.1" x 1.1"

and has good resolution (128x64 which could be 16 x 8 lines of characters 8x8 at a guess).

I have never used one of these before, I guess I would have to program it pixel by pixel, it would not know how to display characters and it would not know how to scroll, or display a cursor or anything else other than the most basic "draw pixel at X Y".

I am right?

Adafruit provide a guide about OLED displays (ones with the SSD1306 Controller) and also a library for them.

First, install the OLED library and the GFX library : Library Then, follow this tutorial, but since your display only has I2C (SDA and SCL) go to the section "Using with I2C". OLED Hookup Tutorial If you want, you can learn more about the GFX library here: GFX Library Tutorial

I have bought 3-4 from ebay the one that has arrived looks like this:

I have already installed the library and the GFX library. I then compiled and ran the example program they give with the library but no fish.

My OLED is at address 0x3C as I discovered by using a scanner sketch.

The adafruit library was using a different address so nothing was working. The OLED is working now.

Except there are two colours on it: a band at the top, maybe 10-16 pixels, which is yellow. Then a black line, it's always black. Then the rest which is cyan.

The example program displays a lot of graphics and it does not matter what it is, the top 8-16 pixels are always yellow and the rest are cyan, with a black line in between.

Edit: looking at the pictures of similar items on ebay it would appear this two colour scheme is done on purpose for mobile phones, at the top you have signal and battery indicators - maybe.

It looks like you don't have any control over the color of the pixel, they are yellow at top and blue at the bottom. In the item's title is says: Serial 0.96" I2C IIC 128X64 Yellow/Blue OLED LCD LED Display Module for Arduino.