That's not something that can be taught. That's all about psychology, reading your opponent, and 'mind games'. It's also about pattern recognition. Some people (such as moi) are kind of naturals, others pick it up easily...Some don't need it, don't bother, or don't care for it....Some folks know the basics behind it. It really depends. The ability to logic, reason, and predict as well as recognize patterns is not something you can easily give a guide on. It's on a person to person basis. Yes, a specific character might benefit more from rolling to the left than standing or going to the right....But that means nothing, because it's up to the player. Like I said....The skills necessary can't be taught in a guide really...Just...when you play, keep an eye out. Notice which direction or response a player tends to take based on what you do next or did...Don't try to continue after. Make it seem like you're going for a tech chase or CG....but don't actually go through with it. Simply observe. One must always do that, even if you've played the person all of the past year or all of the tournaments you've been at together or all of 5 minutes. Failure to play it safe and observe for a bit will only result in you gimping yourself or even in causing you a loss....
This post is hilariously long-winded and unhelpful. He's not asking "how do I read my opponent's mind," he's asking how to tech-chase with Marth. As the other posters have shown, answering this question is about explaining what moves to use, when to use them, and what the ultimate objective should be for tech-chasing with Marth. A pretty basic example is doing dthrow and then fsmash on a space animal when they don't tech.
Obviously fthrow and dthrow are you basic tech-chase starters on a lot of characters. A basic tech-chase is usually to dashdance, follow their roll, and just grab again. This gives you another tech-chase. It's usually a good idea to press z once for damage, since Marth's throws don't do much damage by themselves. Usually I would say the main objective for tech-chasing with Marth is to eventually fsmash or throw them off the edge to start an edgeguard, especially since the more tech-chaseable characters are also usually the more edgeguardable ones.
One of the best techchases Marth has is dthrow-reverse dtilt-pivot grab near the edge against space animals, Falcon, and maybe a few other characters, as someone here already mentioned. If they don't tech they get hit by the dtilt. If they tech in you pivot grab and dthrow again to start over again. If they tech in place you can probably just dtilt again since it has really quick recovery. If you can do this quickly enough without wasting frames it can be really difficult for your opponent to get out of.
In general Marth is probably better off tech-chasing with ground moves, like fsmash, utilt, grab, and dtilt. With good enough reactions and predictions you can usually cover like two or even three options this way. Tech-chasing with a shffl-ed aerial usually forces you to commit to one option, but I've gotten some pretty good results by tech-chasing with shffl nairs that combo-ed into tippers. At high percents you definitely want to go for fsmash tech-chases though since it's the move most likely to get them off the stage.