Stockinette: follow one column of V's
On the knit side of stockinette, each stitch looks like a small V, and each V stacked above another is one more row. Hold the piece flat in good light, choose a column away from the edges, and count V's upward. Lion Brand's row-counting walkthrough counts the loops on the needle as a row too, because they are the row you just finished.
The edge stitches are the hardest to read. A column in the middle gives a cleaner count; check a second column if the first one looked uneven.
Garter: count ridges on the front and the back
Garter fabric looks the same on both sides, and a single ridge on one face does not tell you the whole story. Count the ridges on the front, turn the piece over, count the ridges on the back, and add the two. In garter, count the ridge just below the needle rather than the loops on the needle.
Decide about the cast-on
Most counting guides, including Lion Brand's, do not count the cast-on as a row of knitting. Your pattern may say otherwise, and some cast-on methods leave a row that looks like stitches while others leave almost nothing. Follow the pattern's numbering: if it says "Row 1" after the cast-on, the first row you knit is row 1.
Check the pattern's own words
The Craft Yarn Council's guide to reading a knitting pattern and its abbreviation list explain the shorthand. A pattern can also define its own abbreviations at the start; those win over any general list.
Some patterns number right-side and wrong-side rows separately, or restart the count for a sleeve or border. Write the section name next to the number instead of stretching one count across the whole project.
Mark a row you have checked
Once you are sure of a count, put a removable stitch marker or a safety pin in a stitch on that row. From then on, you only count up from the marker. Lion Brand marks the row where a cable was crossed: if the cable comes every 8 rows and you can see 4 V's plus the loops on the needle above the marker, 5 rows are done and 3 remain before the next cross.
Rows done, or the row you are on
Decide which number you keep and stick with it. "24 rows done" and "on row 25" describe the same place. The trouble starts when one session records the first and the next session reads it as the second. At the end of a session, write the last finished row and what comes next: "24 done. Next: row 25, decrease."
The online row counter keeps a finished-rows count and a note in your browser. The Rowloft app counts the same way by default and has a setting to show the row you are on instead, on the counter and the lock screen alike.