How does one go about clustering data? (I have updated the question following conversation with @whuber in the comments).
My case is as follows: I have around one thousand row vectors of dimension $1 \times 8$. These row vectors are filled with known and non-negative numbers (they are all rational numbers), that can also be zero. In some positions I have $0/1$ variables, but not in all. In principle, they may exist identical vectors. Through utility maximization theory, each row vector is linked to a corresponding profile of preferences (of $8$ dimensions).  
Each position in the vector represents an observable aspect of a product characteristic synthesized with the product selling price, and the corresponding position in the preferences vector represents the utility effect/hedonic price of this characteristic.
What I need to do is to somehow group these vectors to represent preferences profiles much fewer than one thousand. I could then treat each sub-group as a collection of realizations from the same multivariate random vector, and proceed to characterize the distributions.
Strictly speaking, if two vectors differ even in one of the eight positions, and even in the slightest, they represent a different preferences profile.
But I am willing to accept that, for each position, a preference profile can produce a range of values. That is, I accept that "indifference curves are thick" as we say in Economics, or that preferences have some randomness in them.  
From what I understand this is what we call "data clustering", and there are various methods to do this, but this is new territory for me, so I do not trust me to search in past CV posts. 
This is related to research, so please treat it like homework: names of methods and some literature to get me started will really be enough. If any additional info is needed, please ask.
 A: I have compiled the following tiny list of literature for someone who wants to get to know and start to apply Data Clustering. I start by suggestions made in the comments.
1) James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning. New York: Springer. 
2) Hastie, T., Tibshirani, R., Friedman, J., Hastie, T., Friedman, J., & Tibshirani, R. (2009). The elements of statistical learning (2nd ed.). New York: Springer.
These books are not about Data Clustering but cover a wide range of subjects under the label "Statistical Learning".  
The first book appears to be undergraduate-level, and deals with Data Clustering in ch 10, "Unsupervised Learning" (together with Principal Components Analysis). Data Clustering gets 15 pages and two "Labs" (applications with some R-code).
The second book is apparently graduate-level. Here, Unsupervised Learning is ch. 14, and Data Clustering gets 30 pages, obviously more advanced in concepts and a bit more mathematical (but not much), compared to the previous book.  
Both books are officially freely downloadable from the links I provide, in .pdf format and corrected prints.
3) Jain, A. K., Murty, M. N., & Flynn, P. J. (1999). Data clustering: a review. ACM computing surveys (CSUR), 31(3), 264-323.
This is a long review paper. It may be 15 years old, but it contains distilled knowledge of decades of exploring the subject (well-written too). Also, a lot of references to dig deeper.
4) Jain, A. K. (2010). Data clustering: 50 years beyond K-means. Pattern Recognition Letters, 31(8), 651-666.
This is a lecture delivered on the occasion of receiving a scientific prize, so understandably it is more general -and so perhaps a good first taste of the subject for a researcher.
5) Gan, G., Ma, C., & Wu, J. (2007). Data clustering: theory, algorithms, and applications. Siam.
This is a rather recent compendium of knowledge about Data Clustering, including algorithms and code. The authors are commendable for including in ch. 1 a list of 13 surveys and 10 books on Data Clustering, together with more than 100 journals and proceedings that host research papers on the subject. It appears "necessarily" very useful for applications. The link I provide gives only the table of contents - I don't think the book is freely available.  
...and following @gung's suggestion,
6) Jain, A. K., & Dubes, R. C. (1988). Algorithms for clustering data. Prentice-Hall, Inc.
..which is "dated, but introductory, comprehensive, & still good, & which is freely available for download".
A: It seems that your task can be solved with standard clustering algorithms. Try k-means. You choose the number of clusters (k), choose k observations at random and say that they are cluster centers, compute the distance of each observation to each of the centers and assign each to the closest cluster, when done, compute the mean of each cluster, these would be the new centers. Now compute the distances of eachobservation to each center again, and reassing to the closest center. Repeat until no observation moves anymore. Distance function could be the Euclidean distance. 
It is advisable to scale the features before starting, since, if for instance, one feature is measured in 1-1000 and another in 0-1 scale, then the first one would dominate the distance computation, and the second would contribute nearly nothing.
