I think "the short way" for sodium for example is this:
[Ne]3s1
Cafegurl, open up the periodic table from this website in a different window. Now, imagine He was placed in group II next to H and above Be. It sort of belongs there as well as where it is. It's kind of complicated why, but for this purpose, put it right above Be.
Now, find the element you want to figure out the electron configuration for. For example, Cl. Groups I and II make up the "s-block" which means their outermost electrons are in an S orbital. Groups III-VIII are the p-block, and the purple ones are the d-block. The orange ones are the f-block.
Start at H and count to the right. You'll go through two elements in the s-block in the first period, so you write 1s2. The 1 is for the first period, the s is for s-block, the 2 is for 2 electrons. Once you've done this, you have finished the first period, so go to the next. Now you count 2 more in the s-block, so write 1s2 2s2. Then, counting across, you get 6 p electrons in the second period, so you write 1s2 2s2 2p6. Then, the third period; 1s2 2s2 2p6 3s2 3p5. That is "the long way" of writing the electron configuration for Cl.
"The short way" would be to count back to the last noble gas (period VIII element) before your element and then summarize the electrons up to that element with [XX], in which XX is the symbol for the element. For Cl, the short way would be [Ne] 3s2 3p5. He counts as a Group VIII element for this purpose since it has a full valence shell.
The d- and f-blocks are slightly more complex, so make sure you can do the elements up to Ca well before you worry about the rest.
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