How do I use my hacking tools effectively?

Fortify can trigger a network trace, same as hacking a node, so be very careful when using it. Nuke and Slow are nice: using nuke on a "high level" node is useful (nuke will never trigger a network trace), and using slow is nice when you've set off the trace, and are still trying for the capture.

Some general advice:

First thing to remember: if you get unlucky and set off the alarm early, just disconnect. It'll eat up one hack attempt, but that's much better than getting caught.

Second thing: clear the path to the final node first, before you try to take any datastores. That way, you can jump and attack the final node immediately upon a trace starting. It also increases the effectiveness of slow worms, because you can throw a slow worm, finish hacking a datastore, and often still have time to hack the final node.

Third thing: try to avoid high level nodes. You're far more likely to trigger a trace if you hack them, so save them until last, and consider nuking them if you can't hold off on them. This includes API nodes. It's tempting to get them early, but if you set off an actual network trace while trying to hack an API to slow down a hypothetical network trace...You'll look silly.

Fourth and final piece of advice: if you plan on doing a significant amount of hacking, improve your hacking stealth implants. There is no cheaper, more effective way of improving your skill. Even "skill 1" locks can have a dozen or more nodes, and thats a long time to have to stay lucky. Hacking stealth will lower the chances of starting a trace on every node, and that will let you go a lot longer before the trace starts.

Notes on APIs:

Spam: Spam is nice. It lowers the level of the security scan, which increases the time the trace will take hacking through nodes to your entry point. If you're stuck with a lot of high level nodes, it can be worth it to grab Spam before capturing the risky nodes.

Transfer: This one can be annoying. Whenever you hack it (and they're not usually optional) one node becomes easier to hack and one node becomes more difficult. I had a hack attempt once where one of the primary nodes I needed was behind two transfers, and ended up as a level NINE node, while two nodes I didn't give a damn about got reduced. If there ever were a textbook case for using a Nuke, this was it.

Privilege/Authorization: This API usually makes the registry or the datastores easier to hack. If you have more than one datastore, it's almost always worth it to hack this API.

You should also keep in mind that you can hack/fortify/etc multiple nodes simultaneously. Typically, it's not a good idea to do this early on since each node increases the likelihood of being detected, but once you've been detected, feel free to start spaming your hacks around as quickly as you can. Also, once you've been detected you should try to at least fortify the node closest to your starting location, the time bonus you receive can often make a significant difference. So you can start a fortify, and then immediately start your hack on the next node without having to wait for the fortify to finish.

Here is probably the best hacking tip I can give you: Go for the Registries (the tall stack of blocks traces come from) if at all possible. If you capture the registry in a hack you automatically get all the data stores on the network. You can only do this if there is a bidirectional bridge connected to it or a unidirectional bridge leading to it.