The most efficient advertising for a beginning breeder is by word of mouth. This works both positively and negatively. What advertising you will get will depend heavily on how you present yourself to the hedgehog community. If you promote yourself well, then you are going to get positive recommendations. If you come across as someone who is going to have a negative influence on the good of the species, that word will rapidly travel as well.
Prove yourself knowledgeable and experienced. It is a good idea to have a good bit of experience with ownership of hedgehogs before you decide to breed. If you have only owned a hedgehog for a month or two, and then decide to enter the arena of breeding, there is going to be doubt on whether you have enough experience with hedgehogs to deal with day to day issues, much less breeding emergencies. You need to make sure that your knowledge and practices are up to date and accurate. If you practice some technique that is contradicting to popular care methods, you had better be able to back up your information with more than "I read it in a book" or "I saw it on a web page".
Make sure you have the proper motivation- If you enter hedgehog breeding with the intention of making money, or just because they are cute, then that is going to be immediate marks against you. Your primary motivation should be to produce the best quality pets possible, and to help improve the quality of the species as a whole.
Be aware of the laws- Make sure you obey local, state, and federal laws regarding your animals, and obtain all appropriate licenses. Nothing is going to look worse for you than to be fined or arrested for failure to obey the law.
Choose your breeding animals wisely- A very major way to get negative publicity is by creating your breeding stock from pet store animals or rescues. It is important to purchase quality breeding stock from a breeder who tracks pedigrees and is known to be trustworthy and ethical. As well, starting with lines that are known healthy and free of diseases is extremely important. A reliable breeder is going to let you know if there are concerns about the health of a line when you purchase that hedgehog. The more generations of known lineage that are available, the better chance you have of avoiding genetic concerns.
Find a quality mentor- There are several highly experienced breeders active in the online hedgehog communities that are willing to mentor beginning breeders, and answer their questions about breeding practices, pedigrees, ethics, and other aspects of being a responsible breeder. Find one of these individuals, and take advantage of their mistakes and lessons to avoid having to make so many of your own. An experienced breeder is going to have tons of information and useful tidbits that you will probably never find anywhere in writing, no matter how much research you do.
Find a good vet- This does not necessarily mean a highly experienced vet, though that is always nice. If a experienced vet isn't available readily for you, find a vet who is generally experienced with small pets, and is willing to learn from you about hedgehog needs and requirements. When you first go to a vet visit with one of your hedgehogs, make sure that your vet is comfortable handling the hedgehog, to avoid unnecessary anesthesia. Print off web sites that contain quality hedgehog care and health information, but try not to snow your vet under with EVERY single site you see. Choose a few of the most accurate thorough sites, and prepare a small file folder for your vet. If your vet isn't already experienced with hedgehogs, they will probably GREATLY appreciate the chance to learn more about these animals.
Keep accurate and understandable records- A box or pile of papers is NOT going to make it easy for you to find the information you need on short notice. You should be able to keep the majority of your hedgehog records in a 3 ring binder. The system you personally choose is up to you, but make sure it is easily understandable. The method I personally use is pretty simple and easily understood. I divide my folder into 3 main sections. Males, Females, and Retired/Sold/Deceased. This contains all records on animals who spent time in my breeding herd. Each section I sort by age, putting the oldest animals in the front, and the youngest in the back. Each animal gets a plastic sleeve that contains their records. These sleeves contain 4 main forms. Form one contains the animals' name, breeder, date of birth, color, and sex, a section for end arrangements of that animal (death, sold to, etc), and a section for breedings that contains who they were bred to, the dates bred, the date delivered, number of babies born, and number of babies weaned. Form 2 contains pedigree information. My main pedigree form contains 5 generations, with enough space for those animals' full names and colors. Form 3 is health information. This form receives record of all illnesses, medications, vet visits, and other necessary medical history. Form 4 I usually only include in the female's sleeve. This form is for record of offspring. It contains the date of birth of a litter, sire, and then individual offspring sex, approximate color, date sold, and the new owners contact information. I also have a line for any updates on that offspring, including major illnesses, death, or new ownership. My form contains space for approximately 7 offspring, which covers about 2 average litters, so each female would end up with probably 3 copies of this page by the end of her breeding career. For my own ease of reference, I usually put form one facing the front, and form 2 facing the back of the sleeve, with the other two forms in between. This simplifies things because it has the information that you will need most often easily readable through the plastic sleeves.
Pick your customers wisely- I highly recommend to beginning breeders that they screen their customers very thoroughly before you send them home with a hedgehog. This sometimes involves a lot of time speaking to these individuals on a one on one basis. This ensures that you know that they have proper care information available to them, are prepared for the quirks and demands of hedgehog ownership, and are going to in general provide a wonderful home for your baby hedgehogs. In order to do this, you MUST be in one on one contact with your customers. I strongly recommend that you do NOT sell to a pet store. If you have a pet store in your area that is interested in offering hedgehogs, what you can try to do is work WITH them, and let them refer customers to you for a small referral fee. If it is one that you REALLY trust, and that you are able to check in on very frequently, you may consider doing a "demo" in their store, setting up a nice cage with appropriate equipment, and having a hedgehog there for display only, that is NOT for sale. This will get people's attention, show them the appropriate equipment for hedgehogs, and let them know that hedgehogs are available in their area. Then, let the pet store hand out your contact information so potential owners can be screened and educated. Make sure that if you decide to do this, that you check on the health and conditions of your hedgehog often, and if there are any concerns, make sure they get taken care of promptly. Also, make sure that your hedgehog is getting proper socialization while in the store, in order to keep it friendly, which will make it a much more attractive advertisement for your hedgehogs.
Be easily accessible, both before and after a sale- Have a reliable email address that you check often. Daily is GREAT, but at least a couple of times per week is needed. And make sure you ANSWER the emails promptly. If it is something that you have to look up or otherwise can't respond to immediately, send an email stating that you did receive the email, and that you will be responding as soon as possible, and then flag that message to make sure it doesn't get lost before you are able to send a complete response.
Back up what you provide- Come up with a health guarantee that you can live with and still provides security for your customers. Consider a full money back guarantee within a limited time for such things as an owner finding out that hedgehogs are NOT the pet for them, or a vet check that shows an illness that is caused by something before the sale such as a genetic defect, or care related health issue. Plus, offer a replacement if the hedgehog EVER comes up with a genetic illness such as WHS. Beyond this, let your customers know that if at ANY time they find they can no longer care for their hedgehog, that you will either take it back or help them connect with another quality owner for that hedgehog. Make it clear what you offer, and what you expect from them in return (copies of vet records, appropriate care, appropriate housing, etc). Always be available after the sale to answer any questions or take care of concerns to your customers, because keeping these customers happy will provide you lots of positive word of mouth advertising.
Evaluate every word you say or write- People WILL be basing opinions on every statement you make, and what they tell others depends on what you present. While it is impossible to make EVERYONE happy, the more people you do impress, the better your business is going to go. Don't speak harshly, no matter HOW much someone seems to deserve it, because it will come back on you.