Partisans start to show up in July or Aug 41, maybe a little earlier. They then have to man up as they recruit squads from the countryside and recieve supplies that you have to airdrop.
When thier experience and TOE or thier morale and TOE (I can't remember which) equals 90, they start "attacking" the rail lines. In 41, they may (and I mean MAY) cause the German some discomfort as the cross rail lines are connected. After the first mud/winter/mud in 41/42, partisans are worth much if anything.
So it takes a little while for them to man up, get supplies and start operations. And even then, don't expect much except maybe a cut rail line that might cut some supplies to a front if your very lucky.
And if your short of supplies in 42, don't fly supplies to the partisans. If you have supplies to burn, they will increase the German attrition rate a little. Not sure exactly how much, but every little bit helps if you can afford it.