ROCR creates an ROC curve by plotting the TPR and FPR for many different thresholds. This can be done with just one set of predictions and labels because if an observation is classified as positive for one threshold, it will also be classified as positive at a lower threshold. I found this paper to be helpful in explaining ROC curves in more detail.
You can create the plot as follows in ROCR where x is the vector of predictions, and y is the vector of class labels:
pred <- prediction(x,y)
perf <- performance(pred,"tpr","fpr")
plot(perf)
If you want to access the TPR and FPR associated with all the thresholds, you can examine the performance object 'perf':
str(perf)
The following answer shows how to obtain the threshold values in more detail: