Where do researchers get the money to replicate others' work? I'd like to follow up on my previous question. If scientists have to replicate and validate/refute their peers' research, where do the "provers" find funding? 

In my 2 years as an undergrad at a public American university, I've heard of a lot of professors researching new things and/or trying to find funding to research new things, but I've never heard of a professor dedicating resources to replicate his/her peer's work. 

As I explore existing literature for my research project, I see that I could have used existing literature to guide the experiments I did for my project. Along the way, I could have replicated + validated* the existing "new" methods before trying my new method. Is this how researchers usually review their peers?

That is, professor X gets a grant to explore field A. Professor Y comes up with model 1 for field A. Using his own funding, Professor X designs and conducts an experiment to replicate model 1 before testing his own model, model 2. 

Note: I assume my question depends on the field of study since a computer scientist can more easily verify a model + experiment than a chemist.

*Is there a better verb or phrase for replicate + validate/refute? Or does validation imply replication?
In my field (cognitive science), your supposition that replication is primarily pursued by investigators prior to extension is true. For example, I have an idea while reading a paper on learning targeted movements, I first implement the paradigm as described (either an exact replication or a conceptual replication) and then I extend it to test my idea. Thus, the money for this comes from the same places that the money for all research comes from: largely from government allocations and grants, partly from NGOs and industry.

However, there has a been a recent trend--again, in my field, but as part of a larger movement in the social sciences--to improve replicability of results. This has included fostering availability of code for software projects and pursuing independent replications purely for their own merit. Last semester I attended a talk on a set of these replications, which, along with similar attempts from other labs, were pushing to overturn the original result. In these cases, the money to pursue the replication is probably somewhat independent from other projects of the researcher. This means funding agencies would be unlikely to provide a grant entirely for this work, so it is probably going to be supported as a passenger on previously funded work or on University funds (e.g. start up and salaries).