First of all, a consultant is someone you consult because he or she has expertise in a skill you don't. That means a consultant is most certainly going to have plenty of experience in his or her field, and he or she is going to have to have the confidence to both make suggestions and carry those suggestions out without much direction from the client.
Therefore, one of the most important things (even though it may not be directly related to the field of consulting itself) is that a consultant should emphasize strength in his or her interpersonal skills. The consultant must be able to communicate effectively with the client and make him or her feel comfortable with the consultant's presence and the suggestions being made.
How do you present interpersonal skills on a resume such that a client is going to want to call or otherwise contact that consultant and set up an interview? It's better to show rather than tell. So, you can say at the very top in the consultant's skill set that he or she is excellent at interpersonal communications. In the "experiences" or "work history" section of the resume, highlight the jobs and descriptions that utilized interpersonal skills, and say so. For example, saying that the consultant was instrumental as a liaison and go between on a particular project and that this allowed a particular and very important task on a project to be completed is one illustration of just how interpersonal skills caused a particular project to be successful. Again, what you want to do is to highlight a consultant's skill by showing rather than telling.
Remember that the resume is simply a "doorway." It introduces the consultant to the potential employer in such a way that that potential employer wants to meet the consultant. Therefore, it should be an easy read on the first page. If you wish, you can include contact information whereby the potential client can request more documentation such as a representative list of previous clients, references, and so on. However, the resume itself should be relatively brief. Make the first page a brief listing of all relevant information, and if necessary include a second page with more detailed information, should the client want to read about it. However, the client should be able to get everything he or she needs to know from the first page so that simply reading the first page piques interest. The client is going to screen applicants this way and isn't going to read past the first page for a client he or she isn't interested in anyway. So make the first page of the resume do most of the job. The second page of the resume (if you have one) should give more detail but still be succinct.
You also don't want a resume to be a particularly dry or technical read full of jargon. It's perfectly okay to use jargon sparingly, because it shows that the consultant knows his or her field well and knows the language used. However, make sure the resume reads in every day language and is easy to follow. Again, remember that the resume should be presented from the client's perspective. If he or she has to read through a lot of technical jargon and try to decipher it, he or she simply won't take the time. Having a resume that's easy to read and uses relatively simple language shows that the consultant knows the prospective client is busy and doesn't have a lot of time to spend on any one resume. Making the resume simple and easy to read is going to speed up the screening process, and an easy-to-read resume is more likely to get a second look than one that's difficult to decipher.
In short, remember that the resume is there to simply introduce you to potential employers in such a way that the potential employer is going to want to meet that you and want to know more, including scheduling an interview. The resume's only job is to get a foot in the door so that you can do the rest with an interview. Interpersonal skills are among the most important skills a consultant is going to bring to both the interview and to the job, and those can be presented in only relatively brief detail on the resume by illustrating how they were used in particular jobs in the work history or experience section of the resume. However, simply having a resume that's easy to read and yet shows experience in interpersonal communication via work history details is going to be enough. If you can interest a potential employer in scheduling an interview with you, you will be able to market yourself the rest of the way in person.