As far as I understand, collinearity or multicollinearity (hereafter referred to simply as collinearity) cannot be prevented/avoided during data analysis, because collinearity is a built-in "feature" of data. Therefore, a particular data set has certain levels of collinearity (or the lack of). However, collinearity can be prevented/avoided to some degree prior to data analysis, that is, during research design planning or, possibly, exploratory data analysis (EDA) phases. This is likely what Ieno and Zuur (2015) mean by their phrase, which you've cited in your question above.
Potential solutions for preventing / avoiding / dealing with collinearity include using appropriate research designs, which reduce collinearity. However, while I ran across mentioning this approach several times, it was unclear to me which designs exactly are helpful in that regard and why (while StatsStudent mentions one such method - stratified sampling, relevant sources are not provided). Before mentioning other solutions, it is worth to say that sometimes recommended option of dropping predictors is considered as rather bad one - see this blog post or the blog author's book (Baguley, 2012). He also mentions that doing nothing should be considered as one of the valid approaches to dealing with collinearity as well.
Other approaches to dealing with (mainly reducing) collinearity include: increasing sample size and transforming predictors (Baguley, 2012); using principal component analysis (PCA), using simple regression between highly correlated variables (sequential regression) and calculating ratio of correlated variables (Balling, n.d.); a priori modeling and ridge regression (Graham, 2003). While much of literature is focused on dealing with collinearity in multiple regression settings, it should be noted that researchers, who use structural equation modeling (SEM) in their studies, face similar issues of collinearity (Grewal, Cote & Baumgartner, 2004). This is despite the fact that latent variable modeling (LVM) is also considered as an approach to reducing collinearity (see below).
Finally, I highly recommend a very comprehensive paper on the topic by Dormann, Elith, Bacher, Buchmann, Carl, Carré et al. (2013), which contains an excellent overview of methods for dealing with collinearity as well as their comparison via simulation. Those methods include: PCA and other variables clustering methods; already mentioned sequential regression; principal component regression (PCR), partial least squares (PLS) and some other LVM methods; tolerant/penalized regression techniques, include the above-mentioned ridge regression.
Baguley, T. (2012). Serious stats: A guide to advanced statistics for the behavioral sciences. New York, NY: Palgrave Macmillan.
Balling L. W. (n.d.). A brief introduction to regression designs and mixed-effects modelling by a recent convert. Retrieved from http://pure.au.dk/portal/files/14325917/balling_csl.pdf
Dormann, C. F., Elith, J., Bacher, S., Buchmann, C., Carl, G., Carré, G., ..., & Lautenbach, S. (2013). Collinearity: A review of methods to deal with it and a simulation study evaluating their performance. Ecography, 36(1), 27-46. doi:10.1111/j.1600-0587.2012.07348.x Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0587.2012.07348.x/pdf
Graham, M. H. (2003). Confronting multicollinearity in ecological multiple regression, Ecology, 84(11), 2809-2815. Retrieved from http://www.auburn.edu/~tds0009/Articles/Graham%202003.pdf
Grewal, R., Cote J. A., & Baumgartner, H. (2004). Multicollinearity and measurement error in structural equation models: Implications for theory testing. Marketing Science, 23(4), 519-529. doi:10.1287/mksc.1040.0070 Retrieved from http://www.personal.psu.edu/rug2/Grewal,%20Cote,%20%26%20Baumgartner%20MKS%202004.pdf