Much like homemade pasta if you are making your own tortillas instead of buying ready-made ones it's because you want fresh and to be certain of the ingredients; it's not done to save time and effort, and the financial rewards are tiny unless you really make a lot of them.
I probably should just go fool around with presses at a local market and check to see; I hadn't used mine in a while but I did over the weekend and I got somewhat frustrated
Because this is something that many people lose interest in doing you might find a high quality second hand press, with very little usage. The correct dough and consistency also play a big role in obtaining the best results.
Tortilla press geometry problems
... when the plates are fully closed they're touching with basically no wiggle.
When fully closed there needs to be a bit of a gap, some thickness, otherwise you are pressing a wedge shape. Flipping and pressing twice allows less force to be used each time, lengthening the lifetime of your press and reducing your effort, and ensures an even thickness for even cooking.
Instructions from Victoria Cast Iron (1939):
Prepare your masa dough according to the instructions on
package. For this example, we'll use Maseca: just mix 2 cups of
Maseca, 1.25 cups of water, and a pinch of salt. Mix the dough until it has the consistency of Play Dough. Once ready, separate the dough
into 16 small balls about 1.25 inch wide.
Pro tip! Cut a zip-top disposable plastic bag along the corners to
make two square plastic sheets (usually the sandwich size is perfect). Place one of the plastic sheets on the bottom plate. Place a ball of dough slightly off-center, towards the closing hinge. Place the second plastic square on top. (If you do not have zip-top bags, cling wrap or parchment paper can work too).
Close the top plate. The weight of the plate will help you press
down, and the lever will help you finish the press firmly. Not too much force is necessary.
Open the press, place the plastic covered tortilla on one hand, &
peel off the top plastic with the other hand. Flip the tortilla over onto your other hand and now peel back the second plastic square. (Note: They don't suggest pressing twice, as they have a gapped hinge).
You can start putting your pressed tortillas directly on a hot griddle, or on a plate separated with sheets of parchment paper if you prefer to cook or freeze them later.
First, use the correct ingredients. Wheat flour tortillas are rolled with a rolling pin, corn tortillas are pressed; assuming that you are not using the traditional method of doing it entirely by hand.
Corn flour isn't what you want to use (if you are interested in using the correct ingredients and having everything turn out properly). You want to use nixtamalized maize (dried corn boiled in slaked lime, calcium hydroxide) also referred to as ground hominy. Another name for slaked lime, or Cal, is pickling lime (which, ironically, shouldn't be used for pickling).
From Wikipedia's webpage:
In Mexican cooking, hominy is finely ground to make masa. Fresh masa that has been dried and powdered is called masa seca or masa harina. Some of the corn oil breaks down into emulsifying agents (monoglycerides and diglycerides), and facilitates bonding the corn proteins to each other. The divalent calcium in lime acts as a cross-linking agent for protein and polysaccharide acidic side chains. Cornmeal from untreated ground corn cannot form a dough with the addition of water, but the chemical changes in masa (aka masa nixtamalera) make dough formation possible, for tortillas and other food.
You can purchase Maseca (generic name for corn flour) but the Organic Consumers Association has a warning and a list of alternative sources that might interest you.
It is also possible to make your own masa:
Boil cold water (it tastes better than hot water that has sat in your water heater).
Add two pounds of inspected dried corn and bring back to a boil.
Dissolve 5 tablespoons of Cal in a cup of water.
Pour the Cal/water mixture into the boiling water and corn.
Almost immediately the corn will turn a bright yellow color, reduce the heat to a slow boil, then turn off and let it sit overnight.
In the morning the corn will have lost its skin. Scrub it by hand and repeatedly wash in a strainer to completely clean the corn.
You now put the wet corn through a hand grinder twice to obtain the correct consistency, not too fine nor too coarse.
Course ground is useful for tostadas, while too finely ground is useful for nothing.
No one will be too critical it you simply buy ground hominy as it saves a lot of time and messing. Making your own is slightly cheaper but doing so guarantees the quality, and lack of preservatives.
If you eat a lot of maize dishes it's worthwhile to make your own dough. If you eat a lot of tortilla based dishes it's worthwhile to buy a press. If you eat these dishes infrequently it's probably easiest, but not the healthiest option, to buy ready-made.
There's more than one set of instructions being offered for making nixtamalized maize, see: "Easy Nixtamalized Corn Tortillas Recipe", "Nixtamalized Corn maize El Salvador recipe", and "Make Masa: Nixtamalized Corn", amongst many others. Video: "Nixtamalization - How to make Masa and Hominy from Dried Corn" by the Flavor Lab.