To work out how the activity changes, first find the number of half-lives. Number of half-lives = total time divided by the half-life. Each half-life halves the activity, so after one half-life you have one half, after two half-lives one quarter, after three one eighth, and after four one sixteenth.
Worked example: a source has an activity of 640 Bq and a half-life of 3 days. 9 days is 3 half-lives, so the activity goes 640, 320, 160, then 80 Bq. Another example: 960 Bq with a half-life of 5 minutes becomes 480, 240, 120 and 60 Bq after 20 minutes, which is 4 half-lives and one sixteenth of the original.
You can work backwards too. If an activity falls from 1200 Bq to 150 Bq in 12 hours, it went 1200, 600, 300, 150, which is 3 half-lives. The half-life is 12 divided by 3, which is 4 hours.
A graph of activity against time is a falling curve. It is steep at first, then flatter, and it never quite reaches zero. To find the half-life, pick an activity, find half that value, and read the time taken to fall between the two. Repeating this for another starting value gives the same half-life.