The old-fashioned long row isn’t your only option. There’s certainly nothing wrong with planting in rows, just don’t limit yourself to it.
Rows work great if you plan on using machinery in your garden, like a rototiller, and need the empty spaces for the wheels. Originally, tractors would have used the rows. If you’re not going to use any machines like that, there may be little need to go with the row approach.
The problem is that a lot of space is actually wasted with all those empty rows in between your plants. Having a single long row of a single species of plant also makes pollination less effective. Long rows do allow you more walking space and easier access to reach from plant to plant during chores and harvest time.
These days, more and more people are trying the “square foot gardening” method instead. It’s better for smaller gardens that don’t need wheel routes. Your plants are organized in a quilt-like pattern of squares, with your walking paths between groups of squares. For example, one square foot block might hold an array of 16 radishes, or a single head of cauliflower. Check online for measurements for whatever you’re planting.
By using this technique (or something similar), you cut down on all the wasted space between the rows, but you can still easily reach into each grouping of squares to do your chores. It also keeps your plants nice and close for more effective pollination. And that means more produce! Weeds between the plants are kept to a minimum with a good layer of mulch, so you don’t need to worry about getting your hoe in between the closely placed plants.