Transcription factors bind to the DNA to block the transcription of a certain gene, right? But while they are bound to the DNA, do they completely block any transcription of this gene for as long as they stay there or can they also partially block transcription?
Of course it's never 100%. The protein still has a measurable Kd for the DNA, meaning that there's always some part that's not bound (or some time that it's not bound.
Besides that, you're talking about repressors. There are also activators, and they use many different mechanisms. The same regulator protein can even recognize different sequences of DNA and repress one gene more than another. Some can bind and actually recruit a RNA polymerase, some work only while they're binding small molecules.
https://en.wikipedia.org/wiki/Transcription_factor or your molecular biology textbook might be a good place to learn more.
Like Bryan had said in the comments, transcription factors can perform different types of work. Sometimes, binding onto the template DNA strand can cause the RNA polymerase to be activated while sometimes, vice versa.
According to Wikipedia, transcription factors are: "...protein[s] that binds to DNA and regulates gene expression by promoting or suppressing transcription" So both promoting and suppressing is possible.
Transcription factors are combinations of multiple types of proteins, therefore it would depend on what protein you mean.