What is Romeo like at the beginning of Romeo and Juliet? How does he speak of love?

I could argue that Romeo is not any different at the beginning of the play than he is at the end of the play.  Your question though is specific about the beginning of the play, so I'll stick with that. 

Romeo, at the beginning of play, is a giant sack of depression.  He's so annoying in his depression that even Benvolio teases him about it.  

This love feel I, that feel no love in...

I could argue that Romeo is not any different at the beginning of the play than he is at the end of the play.  Your question though is specific about the beginning of the play, so I'll stick with that. 

Romeo, at the beginning of play, is a giant sack of depression.  He's so annoying in his depression that even Benvolio teases him about it.  

This love feel I, that feel no love in this.
Dost thou not laugh?

BENVOLIO

No, coz, I rather weep.

ROMEO

Good heart, at what?

BENVOLIO

At thy good heart's oppression.

Romeo is what English teachers like to call a Petrarchan lover.  This kind of lover assumes such a single minded focus on a yonder fair maiden that he is incapable of seeing anything else.  The woman becomes the man's reason for existence.  It sounds perfectly romantic and like a fairy tale.  Romeo's problem is that yonder fair Rosalind doesn't reciprocate his feelings.  In fact, she would rather be celibate.  Of course Romeo doesn't take that well, so he becomes physically ill at his current "out of love" position.  

Romeo's main problem is that he has a distorted view of love.  Friar Lawrence even calls Romeo on this error.  

O, she knew well
Thy love did read by rote and could not spell.

After Romeo's failure with Rosalind, he has a sort of jaded view of love.  He still has the Petrarchan attitude about love being the pinnacle of his existence, but Romeo also is beginning to think that true love is a mythical impossibility.  It's like trying to grab smoke.  

Love is a smoke raised with the fume of sighs;
Being purged, a fire sparkling in lovers' eyes;
Being vex'd a sea nourish'd with lovers' tears:
What is it else? a madness most discreet,
A choking gall and a preserving sweet.

The quote is from Act 1 Scene 1 and shows that Romeo does indeed believe that love is a real thing, but he sees it as something that is too easily gained and lost.  Not until Juliet shows up does Romeo consider love a physical object worth fighting and dying for.