Getting started
There are some links on the front page about installing Julia if you haven't done that yet.
There are a bunch of useful resources on julialang.org/learning/. In particular, the Julia tutorial at SciPy 2014 is very thorough. This cheat sheet and learn Julia in Y minutes are good quick references. The manual and standard library docs are great too.
To run Julia, from a terminal type julia, which will start a REPL. This may seem like an ancient way of doing things, but it's actually pretty nice. It has color, tab completion, history search, and even supports tab completed Unicode symbols. For example, type \alpha<tab> at the prompt, and \alpha will get transformed to α.
Another choice is using IJulia notebooks via Jupyter (which, confusingly, used to be part of IPython.) Notebooks are really nice for working interactively while building up an analysis and work like IPython notebooks if you're familiar with those. Installation instructions available here.
If you want an IDE, there's Juno which is really nice. Don't bother with Julia Studio if you come across it. It is out of date and no longer maintained.
Like R, you can access Julia's help system by typing ?name in the REPL. The @edit macro is useful if you want to see the code of the function you're calling. For example, @edit factorial(10) opens the method of the factorial function for Ints (the type of 10) in an editor.
Importing data
To get data in to Julia, the easiest way might be via a CSV file. In base Julia, there's the readcsv function, or more generally readdlm for other delimiters. Check ?readdlm for docs.
Julia does not have built in support for missing data, but it is supported by the DataArrays.jl package which is used by DataFrames.jl.
DataFrames.jl provides the readtable function which can read a CSV file among other things and creates a DataFrame object. A DataFrame in Julia is sort of like a data.frame in R.
There's also HDF5.jl if you want to use the HDF5 format for moving data around.
Regression and prediction
The estimation procedures in TargetedLearning.jl take as input things like estimated conditional means or probabilities. The Julia ecosystem has packages for fitting models and machine learning methods, but they are generally not as mature as those in R or python.
GLM.jl can be used for fitting generalized linear models and GLMNet.jl fits glms with L1 and L2 regularization. Orchestra.jl fits heterogeneous ensemble estimators using cross-validation. You might be able to find other useful packages on pkg.julialang.org.
For simple linear regression models, linreg is available in base Julia. For logistic regression, this package provides the lreg function.
For R and python users, at this point it may be easier to fit initial estimators using tools in those languages. PyCall.jl allows you to call Python functions from Julia, so something like scikit-learn can be used. It's very mature and used in many other packages. RCall.jl is less mature, but it lets you do something similar with R.
Plotting
It's always nice to be able to plot things without switching languages. Julia has a few choices. Gadfly.jl and PyPlot.jl are two good choices listed here. There is also Winston.jl which is not listed there. It's sort of like Matlab's plotting system, and nice for simple and quick stuff.
Example
Throughout the user's guide, we'll use the Lalonde dataset. It is originally from Robert Lalonde, "Evaluating the Econometric Evaluations of Training Programs," American Economic Review, Vol. 76, pp. 604-620. 1986. This section we'll go through a few ways of loading that data set.