Why would I use any MC technique other than basic sampling I'm trying to learn sampling techniques. Lots of tutorials say that they are useful when "you can't sample directly from the pdf...."
q1)
If I have the algebraic form of the pdf can't I always sample from it?
If I didn't have the algebraic form then I couldn't do anything anyway. What do they mean by this?
q2)
Why would I bother with something like importance/gibbs/mh sampling when I can just sample directly from the pdf with random numbers like this:
for i=1:1000

    rv = rand;

    scatter(rv,betapdf(rv,3,6));

end

This gives me a perfect form of the 3,6 beta.
The importance sampling technique produces a worse pdf approximation.
What am I missing
 A: I'll tackle your second question first. Your method doesn't sample from the beta distribution, but you're sort of right in that there are simple methods that work well when you know the pdf. Say that the pdf of the beta(3, 6) distribution is $p(x)$ and you want to know $y \equiv \int_0^1 f(x) p(x) dx$. Then you could do something like this:
n_draws = 10000;
x = unifrnd(0, 1, n_draws, 1);
px = betapdf(x, 3, 6);
y = f(x)' * px / n_draws;

Or even better, don't sample:
x = 0:.0001:1;
px = betapdf(x, 3, 6);
y = f(x) * px' / length(x);

However, this only works on the beta distribution because its support is on $[0, 1]$. You wouldn't be able to apply such a method to a distribution with unbounded (or unknown) support. However, if you know the CDF, you can use inverse transform sampling to take draws.
Now for your second question: If we know the PDF, why would we need a complicated sampling method? Often, you may know the PDF only up to a constant. Then you can't use inverse transform sampling to take draws. However, you can still use a method like importance sampling or Gibbs sampling.
For example, let's say we want a function of the posterior distribution in a Bayesian model, where $\theta$ is the parameter of interest, $x$ is data, and $\Theta$ is the set of all parameters in the support of the prior:
$$
p(\theta | x) = \frac{p(x | \theta) p(\theta)}{\int_\Theta p(x | \theta') p(\theta') d \theta'}
$$
It may be easy to compute $p(x|\theta) p(\theta)$, but the denominator may be a lot harder. However, you can just note that $p(\theta | x) \propto p(x|\theta) p(\theta)$, and use that fact to use importance sampling, Gibbs sampling, or some other Markov Chain Monte Carlo method to take samples from $p(\theta | x)$. Then you can use those draws to compute a posterior mean or another function of the posterior distribution.
A: *

*That is not a sample from a beta(3,6) distribution.  It is a graph of a uniform variable vs the beta PDF.  For this to be a sample of the beta(3,6) the histogram or density plot of your putative sample (not a scatter plot) should converge to the beta(3,6) PDF.  You sampled, $U$, a uniform random variable, and then applied a transformation (the beta PDF function) to it.  Here's what the density of  of this transformed random variable looks like in black (D(beta_pdf(U))).  In red, I am showing the the beta(3, 6) function.

Right away, you can tell something is amiss, because betapdf(U) is as large as 2.5, while we know that a beta random variable lies on the interval [0,1]. 

*Generally, you do have the algebraic form of the PDF, up to a constant.  But not knowing the normalizing constant of your density means you are stuck!  For the beta distribution, the normalizing constant has a well-characterized (though non-algebraic!) expression.  In general, MCMC is the way to avoid evaluating a complicated, high-dimensional integral, which is how you would generally calculate a normalizing constant.

*Even if you do have the normalizing constant, you still need a way to sample, ie, rejection sampling or as another answer points out, the probability integral transform.

