user64: In the middle and the end of a chess game, there are visible consequences to almost every move you can make, there are more constraints limiting what is logical to move, and it is fairly straightforward to see what you did wrong when you analyze the game.
At the beginning of the game, it seems like there is a tremendous number of possible ways a game could progress--and not very many of the moves have any immediately tangible consequences. Because of this, I usually have no idea what I should do in the beginning of a game.
Are there any things I should be thinking about at the beginning? Up to date, I've just been moving pieces haphazardly until what I need to do becomes obvious.

user17: According to world champion Capablanca, in "Chess Fundamentals," your first priority is to get your pieces out as fast as you can. If White, you might take a detour to try to hinder black's development, in order to maintain your relative advantage; if Black, you need to find tactical ways to parry White's threats.
Otherwise, you should be looking to concentrate your pieces, particularly in areas left weak by your opponent. Did s/he leave parts of the board undeveloped or undefended to favor a few pieces? Then try to find a way to take advantage of that fact. Perhaps the opposing king is inadequately protected, and can be attacked. If not, your opponent may have started an a attack prematurely and left the so-called "center" (of the board) insufficiently guarded. If so, a successful center counterattack will stop most attacks. 

user109: 
Develop your pieces, not Pawns
Try not to move the same piece more than once in an opening unless
you really need to. Gain control of the center Castle your king
Develop/Connect your rooks Don't move too fast or you will blunder.
Take your time and view the whole board.


user70: Memorize three openings to several moves.  I recommend, as white, one opening, probably king-pawn opening.  Then memorize two openings as black so you can react your opponent's K- or Q- pawn openings.
For example, I prefer a King's Indian Defense to 1. d4, and the Caro-Kann Defence to 1. e4.
When playing white, I play a Queen's Gambit.
Memorize the most popular lines to 5 or 6 moves.  Then study them to find out why those moves are popular.
And to answer your question directly, you should be looking to take material or kill the guy's king, starting on move 1 (paraphrased from Bobby Fischer.)  Good piece development is a great start.

user65: Agree with @JaredDef's answer which covers the big ideas. Some more specific opening strategies for beginners can be found here:

make your first move with the
pawn in front of either your King or Queen 
make good developing moves, and generally develop your
Knights before your Bishops 
try not to move the same piece twice in the opening 
your King's safety is crucial; castle early if you can
don't advance more than one or two pawns in the chess opening, and definitely not a pawns in front of your castled King
when you develop your pieces, try to make moves which threaten something
don't bring your Queen out early


user66: There are a few regular things you should fight for out of the opening

Control of the center
Development of pieces
Early castle
Space

So basically you want to get as many pieces out as quickly as possible, while attempting to control the center (the four middle squares and to a lesser extent the next ring of 12 squares). While not all opening strategies revolve strictly around these principles, it is found in the majority of games and especially good rules to play by when starting out.
EDIT: Keep in mind these are not all rigid rules. I would also like to respectfully disagree with Tony. When starting out, memorizing openings is the very last thing you want to do. Feel free to look through an openings book (The first, and very amazing, book on openings that I read) or database. However do not seek just to memorize and spit out moves until you reach a position you haven't actually thought about.

64: <p>In the middle and the end of a chess game, there are visible consequences to almost every move you can make, there are more constraints limiting what is logical to move, and it is fairly straightforward to see what you did wrong when you analyze the game.</p>

<p>At the beginning of the game, it seems like there is a tremendous number of possible ways a game could progress--and not very many of the moves have any immediately tangible consequences. Because of this, I usually have no idea what I should do in the beginning of a game.</p>

<p>Are there any things I should be thinking about at the beginning? Up to date, I've just been moving pieces haphazardly until what I need to do becomes obvious.</p>
 17: <p>According to world champion Capablanca, in "Chess Fundamentals," your first priority is to get your pieces out as fast as you can. If White, you might take a detour to try to hinder black's development, in order to maintain your <em>relative</em> advantage; if Black, you need to find tactical ways to parry White's threats.</p>

<p>Otherwise, you should be looking to <em>concentrate</em> your pieces, particularly in areas left weak by your opponent. Did s/he leave parts of the board undeveloped or undefended to favor a few pieces? Then try to find a way to take advantage of that fact. Perhaps the opposing king is inadequately protected, and can be attacked. If not, your opponent may have started an a attack prematurely and left the so-called "center" (of the board) insufficiently guarded. If so, a successful center counterattack will stop most attacks. </p>
 109: <ul>
<li>Develop your pieces, not Pawns</li>
<li>Try not to move the same piece more than once in an opening unless</li>
<li>you really need to. Gain control of the center Castle your king</li>
<li>Develop/Connect your rooks Don't move too fast or you will blunder.</li>
<li>Take your time and view the whole board.</li>
</ul>
 70: <p>Memorize three openings to several moves.  I recommend, as white, one opening, probably king-pawn opening.  Then memorize two openings as black so you can react your opponent's K- or Q- pawn openings.</p>

<p>For example, I prefer a King's Indian Defense to <code>1. d4</code>, and the Caro-Kann Defence to <code>1. e4</code>.</p>

<p>When playing white, I play a Queen's Gambit.</p>

<p>Memorize the most popular lines to 5 or 6 moves.  Then study them to find out why those moves are popular.</p>

<p>And to answer your question directly, you should be looking to take material or kill the guy's king, starting on move 1 (paraphrased from Bobby Fischer.)  Good piece development is a great start.</p>
 65: <p>Agree with @JaredDef's answer which covers the big ideas. Some more specific opening strategies for beginners can be found <a href="http://www.chesscentral.com/Chess_Strategy_a/201.htm" rel="noreferrer">here</a>:</p>

<ol>
<li>make your first move with the
pawn in front of either your King or Queen </li>
<li>make good developing moves, and generally develop your
Knights before your Bishops </li>
<li>try not to move the same piece twice in the opening </li>
<li>your King's safety is crucial; castle early if you can</li>
<li>don't advance more than one or two pawns in the chess opening, and definitely not a pawns in front of your castled King</li>
<li>when you develop your pieces, try to make moves which threaten something</li>
<li>don't bring your Queen out early</li>
</ol>
 66: <p>There are a few regular things you should fight for out of the opening</p>

<ul>
<li>Control of the center</li>
<li>Development of pieces</li>
<li>Early castle</li>
<li>Space</li>
</ul>

<p>So basically you want to get as many pieces out as quickly as possible, while attempting to control the center (the four middle squares and to a lesser extent the next ring of 12 squares). While not all opening strategies revolve strictly around these principles, it is found in the majority of games and especially good rules to play by when starting out.</p>

<p>EDIT: Keep in mind these are not all rigid rules. I would also like to respectfully disagree with Tony. When starting out, memorizing openings is the very last thing you want to do. Feel free to look through an openings book (<a href="http://rads.stackoverflow.com/amzn/click/1857443497">The first, and very amazing, book on openings that I read</a>) or database. However do not seek just to memorize and spit out moves until you reach a position you haven't actually thought about.</p>
