Slow and Steady Definitely Wins This Race:
Unlike PCB builds, stripboard doesn't come with a nice printed layout on the board indicating exactly where each component goes. I always check the placement of cuts multiple times, marking the cut location with a sharpie once I am confident the placing is correct. If the cuts are wrong, the build will fail.
After cutting the board, I mark the top-left corner with a sharpie for reference. It's easy to get the orientation confused otherwise.
Once the cuts are made, I test continuity across the cuts with a multimeter. Sometimes, a tiny trace of copper remains which again would lead to problems. Much easier to check the cuts before adding components. Slow and steady again.
Next I add links to the board. I measure location by counting from different directions as a cross-check. A link might start 5 across and 6 down from the top-left. Mark that hole with a sharpie. Then check it a second time, perhaps from a different direction. Going slow and triple checking the link placements helps the rest of the build go smoothly. Once you get some trusted landmarks on the board, placing the rest of the components gets much easier. Instead of counting 17 across and 9 down from the top-left, you can do things like "5 across and 1 down from the top of that link".
Final slow and steady tip: solder just one component at a time. Before soldering, double check location. After soldering, inspect the solder joins (I use an illuminated desktop magnifier for this) before clipping the leads. You want a nice shiny joint that flows nicely onto the board. This lets me catch unintended solder bridges (across adjacent tracks) early. The other common problem is too much solder causing the solder to flow along the track and cover the next hole on the same track. Again, easier to catch and fix early (although if no component needs to use the blocked hole I tend to leave these alone).