Generally, all you should have to do, assuming that the people did it right when they installed your GPU.
1) Put the GPU in the right slot.
2) Make sure BIOS either is set to 'Auto' or 'PEG first'. Hopefully not 'PEG only' which means you have to get into the BIOS settings yourself as the IGP won't init.
3) Install the drivers.
To get the IGP going, I'll assume that you pulled the dGPU out, right? At that point, just plug the HDMI cord in, power on the TV/Monitor, then power on the computer. It should (assuming 'AUTO or PEG FIRST'), check the PCIe slot, find nothing, check the IGP, find an output available, and init it. The screen should light up and start displaying.
Now, if it doesn't work, they might have set 'PEG only' which means IGP is effectively disabled. Two ways around that if you don't want to mess with it overly much and you have a simple system.
1) Find and change the bios settings. For most BIOS setups, you'll have a CPU section, a Graphics section, Boot setups, RAM settings, then save and exit. A LOT depends on what exact motherboard you have, so at this time a detailed guide just isn't possible since you didn't give full specs.
2) Just reset it to defaults. If they only changed your IGP settings on installing it, in the 'save and exit' section, there's usually an option 'restore defaults' (sometimes either optimal defaults or fail-safe defaults). Use the optimal defaults. This usually enables IGP/AUTO settings.
3) Hard BIOS reset via RESET_CMOS jumper or pull the battery backup. Just as it says, there's a jumper that if you short the pins, resets the BIOS to factory default (IGP enabled), pulling the battery (CR2032 flat battery usually) does the same.