I have a 0.91 inch display with a 4 pin I2C connection. I then realised that I needed to use a 0.86 inch display with the connector in the above image. I have searched on google on this but nothing has come up. Are there any suggestions on how to connect this? Below is a part of the datasheet if that helps.
If you need a connector, the 0.62mm pitch connector is an oddball, apparently only available from a couple of Chinese manufacturers, eg. Wenda LW06121. Suggest you ask the display supplier to source them for you. They list similar connectors for a very reasonable price. However the datasheet refers to "Soldering Type FPC" so it looks like it's mainly intended to be soldered to the PCB directly (and being single-sided that's not a problem).
As you can see, there's a couple of charge-pump capacitors C1/C2, some bypass capacitors, a resistor to set the OLED current, and the usual pullup resistors on the SDA/SCL I2C data and clock lines.
There's also demo code available.
Find a datasheet for your specific display module. These 128x32 modules come in different variants with pinouts capable of SPI, IIC and other communication protocols. The datasheet for those usually contains a reference breakout to each available mode with capacitor values and recommendations.
In my project I’ve used one 128x64 module with 30 pin flex cable. And breakout was rather complex. I would not recommend using dayasheet of any other modules even if they look similar as recommended breakout schematics and component values can be quite different.