It all starts with DIGITIZING: 
Embroidery Machines use commands to tell the needles where to go and what to do, the action of encoding these commands is called "Digitizing".
Logos, designs, fonts must all be digitized before they can be embroidered. However the good news is that embroidery machines come with some fonts already embedded in them.
The pictures below show the available / pre-digitized fonts that you can choose from. This pictures show the actual embroidery sew out and is not computer generated.
Projects of just plain text and no logos such as embroidery names on Christmas stockings, initials on Robes, names on lab coats or simple text on any garment such as graduation sashes do not need digitizing as long as you choose from the  pre-digitized fonts.

Puff or 3D / Raised is another method of embroidery. Here are pictures of an actual image and the outcome in PUFF.
There are two circumstances when an image cannot be Puff embroidered:
A - The image is too small / narrow hence cannot be done as a PUFF embroidery. See the text "CLOTHING COMPANY". The PUFF surface must be minimum 3/16th of an inch wide (about 5 Millimeters).
B- The image is too wide which will result in the thread to be loose and the embroidery is beyond the machines capability. 

Font / Text size:  
Needles are too thick to create or write very tiny and thin texts, even lines have to be at certain thickness. See the word Success in this picture, the lower case letters "height" is 1/8".
That's why the traded marge (R in a circle or TM" are hard to embroider when its too small. 
Gradient / Fade out:  
Although it is impossible to get a perfect gradient outcome yet these actual images are samples of what we've been able to achieve.
The larger the embroidery area, the smoother the transition.  
Embroidery cost:
It is all about number of stitches and not number of colors in your design therefore to give you correct pricing, we need to:
1- See your design and know how large "in inches" you want the design to be embroidered.
2- How many garments.
3- What style garment: Shirts, Baseball caps, Beanies, ....... .