How to determine whether changes of an allele's frequency are due to genetic drift or selection?
Is there a way to disentangle selection from drift 

Yes, there are actually many ways...so many so different ways that it is impossible to correctly answer this question. Hopefully, below answer will give you some appreciation of why there is such a diversity of methods and wil give you sources to further your knowledge on the question.

It depends upon the data you have

The answer very much depends on the data you have in mind. Are you looking at a


panmictic population
a structured population
are you comparing a large number of lineages along a phylogeny
do you have information about a proxy for fitness in this population
can you perform an evolution experiment (depends a lot on the generation time)
do you have genetic data that are temporally separated
...


Also, what type of selection are you thinking of? 


balancing selection
Are you trying to find epistasis for selection
Are you looking at some form of balancing selection
Local selection
...


Also depends upon whether you have data about potentially correlated variables such as


phenotypic data
ecological data


There are tens (or even hundreds of methods esp. when having data about related lineages) under each bullet point above, so your question is definitely quite broad.

Source of information

Statistical tests that test to the null that there is no selection are often called "test of selective neutrality". You might want to read Nielsen 2001  and Nielsen 2005 to get an overview of tests of selective neutrality in panmictic populations.

You might want to have a look at this answer, this answer and especially this answer.

What does it take to understand the methods for disentangling selection from drift?

Understanding the tests of selective neutrality can be a bit demanding as it requires having good knowledge in classical statistics, bayesian statistics, MCMC, Approximate Bayesian Computation and even machine learning algorithms. It also requires good knowledge in population genetics (typically incl. coalescent theory) and statistical phylogenetic.

A specific example

Unfortunately, I can't think of any specific example of a test which is really easy to grasp without a priori knowledge. A classical, not too hard and historically example test for neutrality in panmictic population is the used of Tajima's D (which derivation require basic knowledge in branching processes). You might want to learn about it to have a specific example. I recommend Gillespie's book Population Genetics: A Concise Guide to learn about this test. More book recommendation can be found here.