Non-embroiders usually believe that you need an embroidery hoop to do hand embroidery. Not true!
In fact, most experienced embroiders prefer to use the jab and pull method, even when less confident stitchers need more stability.
These wooden or plastic devices hold fabric stretched flat so that stitches are not pulled too tight because tight stitches cause wrinkles.
Some people will use a small round lap frame as a cross stitch frame for display, but it might not necessary when working in cross stitch depending on the type of fabric you are using.
Do NOT use a hoop or frame...
DO use a hoop or frame...
The difference in a punch needle embroidery hoop is that it needs an extra lip to hold the fabric as tight as a drum. There are also hoops available that have small teeth, or you can make your own wooden frame and tack the fabric.
Be careful to use a hoop large enough to contain the entire design at once. Otherwise, you'll have wrinkles across your work!
There are now special rounded quilting frames available that do not leave unsightly wrinkles.
Also, when stretching fabric in a hoop, make sure you stretch in all directions evenly. Keep the fabric an evenweave. Don't distort your pattern!