Damansara is big. which part in particular?
Basically USJ is sandwiched between Subang Jaya in north, and putra height in south, Puchong in the east to southeast area.
Crossing subang jaya (ss 12-ss19) is a nightmare in the morning during weekdays. there's only 2 bridge that you can cross from USJ to SJ (coz Kesas separating both area).
Once you get into Subang, you need to cross the federal highway. 2 ways....exit from Empire Subang side or the 'highway in the sky' from Summit direction towards Subang Airport. From there, you can use the road to cut thru Tropicana Gold Club area to KD.
Again depending where you want to go.
If you stay in the end of USJ, near Main place area, the other method is to use the Elite highway to leads to NKVE. But then you need to 'sabar', as the road can be packed during weekdays.
If I were you, and you have other choice, avoid Subang / USJ.