In terms of when to start the “Doing” this would be my general recommendation, though it obviously depends on the kid and family (i.e. a sport season or theater production or other things that mean things need to be pushed earlier or later).
NOW
If you’re in California or a state where it’s hard to find nearby testing sites, I would try and schedule a test date as soon as possible (dates for SY24-25 are open for registration now). (Not to take the test as soon as possible but to register for the desired date as soon as possible in the hopes of not needing to travel far to test.)
If your kid tends to be a good test taker, then I would have them do some test prep for the PSAT which juniors take in October. There are free resources like Khan Academy, and posters may have other suggestions as well. If your student is among the top test-takers in your state, your kid may then qualify as a National Merit Semi-Finalist, most of whom go on to become National Merit Finalists (NMF). There are schools that offer very big automatic scholarships for NMF students, like a full ride.
FALL
Even if a kid is not a great test taker, the October PSAT is a chance to practice on a test that will be similar to the SAT, and familiarity with the test is one of the things that can raise one’s score. Additionally, it can give you a floor of what kind of schools your kid might be competitive for (though SAT scores usually end up higher than the PSAT equivalent score…as kids will often have 6+ months of additional education under their belts to improve before taking the test).
The next thing I would do is to start some casual college visits. If there are any colleges nearby, visit those. Or if you’re visiting family or on vacation and there’s a college nearby, visit it. The idea here is to try and visit a range of schools so your kid can get a sense of preferences in terms of a small/medium/large enrollment, urban/suburban/college town/rural location, vibe of campus, etc, not whether that specific college is a fit for your kid. Once your kid has a better idea of what they’re looking for, then you can start in on researching actual schools that could be possibilities.
Also, talk to your kid’s English teacher (at open house/parent night and/or in other communications) about whether or not they will work on the Common App essay topic before school gets out. Mention that many schools do it after state/AP testing. Basically, put it on their radar as something that would be useful. Repeat after the return in winter break and then again in early spring if you don’t get an affirmative answer earlier on. 
And if you did get an affirmative early on, send a confirmation email in the spring just as a reminder.
WINTER/SPRING
When doing the college search, I highly recommend starting from the bottom up. So look for the sure things for admission first. Make sure your kid has at least one (and preferably at least two) that they would be happy to attend for four years.
If you plan to travel for college visits, I would try and ensure that you’re not just traveling to visit reach schools. If anything, I would give the priority to likely and target schools. If the focus is solely on reach schools, kids will get the impression that those are the only schools that the family values or thinks are worthwhile, and if a kid ends up preferring a likely admit or not getting into the reach schools, then it can be a source of tension.
And overall, let your kid be a kid. Let them follow their interests and socialize with their peers. Find special time for family activities because before you know it, the kid won’t be living with you anymore. Make sure that college conversations are not stressing the kid.
Some families find that having a designated time as the exclusive time for college conversations helpful if the conversations are become a source of frustration in the house.