Assuming you are applying to schools which require (or recommend) standardized tests for admission, you should start thinking about them relatively early. I highly recommend that you avail yourself of the opportunity to take the PSAT and/or PLAN (pre-ACT) at your school in the fall of 10th grade. Your test score will not be counted toward any future college admission process. I advise taking it as it will give you a close-to-real experience of how you'll deal with taking the SAT and/or ACT.
In the fall of your sophmore year you'll still have up to two years to work on areas of weakness. This may seem like a crazy long time, but if vocabulary and reading comprehension are your downfalls, you'll need time to build your vocabulary and get enough reading under your belt to improve your comprehension. If you really struggle with the reading and vocabulary on the SAT, recognize that you are really, really going to struggle in college level classes. This is something to get to work on now so that you don't drown in reading that's over your head your freshman year (or in AP classes). The math and grammar sections can be quicker fixes for most students with a good foundation, but still take time: time you will not have in the spring of your junior year.
So, take the PSAT/PLAN in 10th grade and use your results to work on areas you struggled with. At this point you may decide that you're only going to take one of the tests as you did much better on one than the other or that you want to take both.
Most students take their first SAT in March or May of their junior year and then take two SAT IIs (don't know what these are? check my archive.) in May or June. (Note- Now that the UCs are not requiring SAT IIs we may find that this advice changes. I'm not sure how many schools will follow suit and how many UC majors are going to 'recommend' taking them still.)
The SAT is administered in Oct, Nov, Dec, Jan, Mar, May and June each year. Therefore you have six reasonable dates to complete up to four tests assuming you don't take anything more than once, and almost everyone takes the SAT twice. Assuming you take the March SAT and do need to take SAT IIs, you can take up to three on a given test date, but I recommend only taking two. So, you'll take two SAT IIs in May which will leave the June test date open to either take a third SAT II option to see how you do, or to retake one of the previous tests. Your junior year will be crazy, but you'll probably be best prepared for these tests at the end of that school year. If you're not happy with your results, study over the summer and take the SAT again in October, leaving the Nov. and Dec. dates open for last ditch efforts which will hopefully not be necessary. Notice that the SAT I and SAT IIs are administered on the same dates and it is not possible to take the SAT and any SAT II on the same date.
The ACT is generally administered in the same months, but usually not on the same Saturday. This can be important if you've gotten yourself in a bind. Say you're very unhappy with you SAT score and on top of that you didn't realize you had to take SAT IIs and it's Nov....of your senior year. This is the time to figure out if the ACT is a good option for you if ever there was one!
Both tests have accomodation (usually on the Sunday) for students who can not take the Saturday test for religious reasons.