You must be worried sick given your family history, but if it's any consolation I did read somewhere that no link has been established between a family history of cancer and increased risk of CC. It's that pesky HPV which by and large ends up causing the changes.
Your smear came back moderate, which is normally CIN2 I believe. This is not the most severe level of changes, so that's a little bit less to worry about. At the colposcopy, they will apply solutions to your cervix to see where the abnormalities are, then probably take a biopsy to confirm the exact level of the changes. Brace yourself for some waiting, because normally the biopsy results take about 4 weeks to come back. They give a clearer picture of the level of abnormality - for example my smear was borderline with high risk HPV, but the biopsies came back with mostly mild (CIN1) with some small areas of moderate changes (CIN2).
The colposcopy is not that different from a smear test really, it just goes on for a bit longer. I didnt find any of it painful, just a bit weird because someone is putting things on your cervix and no-one normally touches that! It was OK though.
If your biopsy results come back mild, they will probably ask you back in a year, as mild changes often sort themselves out. Any higher than that, they will no doubt do a LLETZ procedure to remove the abnormal cells. Apparently in 95% of cases, this is all you need to both remove the cells and kick-start the body's immune system into fighting off the HPV infection too.
Try to remind yourself that you have moderate cell changes, it's not cancer, and it's a good thing that we have regular smears in this country so that when this does happen, the bad cells can be dealt with long, long before they are able to become a problem :-)
hugs and hope all goes well this morning