Tally all of the students' scores. Choose a number of points, perhaps the number of points needed to raise the lowest score to a passing score, and add those points to all of the scores equally. Note that this make the highest possible score over 100 hundred points.
Choose a scale factor to represent the variable "F." F should generally equal anywhere between .6 and .9, with the smaller number causing a greater curve in grades. Take the first score, let's say it's 75, and subtract it from 100 to get 25.
Multiply the number you get, in this case 25, by F. Let us say that in this case F is .9, meaning that you must multiply .9 by 25 to get 22.5. Subtract the number you get, 22.5, from 100 to get your adjusted score of 77.5, just a few points higher than the original grade. The mathematical equation for this method of curving is new score = 100 - F(100 - original score).
Decide what extra credit work you will give later on in the course beforehand, but avoid telling students that there will be make-up work. This will encourage students to be diligent and to do their work well since they won't know that there is a fallback option. If all your students do well, there may be no need to hand out extra credit items at all.
Select five different types of extra credit assignments that reflect course material and that vary in subject or format. Present these five options to your class and allow them to choose which they would like for extra credit work. This may improve the chances of students doing well on these assignments since they get to choose what they want to work on. It also keeps you in control of the assignments.
Establish an extra credit deadline beforehand and make it clear to students that they must have all of their work turned in by that date and time. Do not accept mediocre excuses or late assignments on extra credit work, especially if students had ample time to turn them in.
Grade the extra credit assignments just as you would grade all the other assignments. Avoid grading lightly, as this would be unfair to other students who worked hard, did well and did not need extra credit. Also, avoid grading the work too harshly, as it may defeat the point of giving out the extra credit.