This is a totally nerve racking thing to do; you'll feel that you're not good enough yet and things are bound to go wrong .  You'll be nervous and things will sound very different than you're used to at home.

So, for your first time, should you go for playing in a club or at a house party?  Starting in a club is a lot more trying on the nerves, after all people have paid their hard earned cash to get into the place.  But then sometimes pressure helps, so this is entirely up to you - I first played out in a club, and am glad I did (I wrote a report of my first time experience if you're interested).

As it's your first time, you'll be playing early in the night anyway - most probably first.  This is really good, as there probably won't be many people around to hear your efforts - less pressure!  You might even find that there's no-one around at all when you start which makes things really easy on the nerves.

Lots of things will be very different when you play out for the first time - you'll probably be really used to using your own system and this may be your first time on something different.  You'll find that the sound is totally different than you're used to, the mixer will be different, the decks will be crappy with coins glued to the cartridges and the slipmats will be awful (I normally take my own with me).

If that's not enough, you'll be petrified and your hands will be shaking - but this is all part of the fun - it takes time and experience to be able to relax behind the decks in public. You therefore want to do all you can to make things as easy as possible for yourself:

Practice your set
Experienced DJs will pick their tunes as they go along, watching the people on the dancefloor and choosing the musical direction as they go along - gauging the response of all those people out there.  Unless you are well practised, brimming with confidence and have your beatmatching totally sussed you might want to have a pre-prepared set that you know works.

When choosing the records for your set, try and choose them so that the music progresses through your set, then things will flow nicely.  Also, avoid any that you find hard to mix; you'll be under enough pressure as it is without making things unnecessarily hard for yourself.

When practising, don't always do the same mix each time - play around with bringing in the new record at different times and in different ways.  You never know, you might find better ways to do the mix.  This will also help when you find you have a room full of people and you were so nervous that you forgot to start the record at the time you always start it.  If you've tried different ways of mixing between the two, you're less likely to end up in a blind panic.

Crib Sheet
I've not noticed anyone else doing this, but as I was pretty crap at beatmatching the first time I played out I used a crib sheet.  This had all the tracks (with the bpms and the pitch control positions for each one) listed on it.  I also used highlighters (and writing on the records in big letters with a thick marker pen) to remind me if the record had two tracks on it so I'd remember not to let it run into the gap between the tracks.

Equipment
If you can, find out what features you'll have on the mixer you'll be using and practice using only the same features on yours.  If you can beg/borrow/steal the same sort of mixer you'll be using in the club from someone or at least have a go on one first then at least you'll know where all the knobs and switches are before you get there.  Also, if you don't have Technics, it's probably a good idea to have a practice on some first so you know beforehand what they're like - specially if you've only used a belt drive deck.

Also, get to the party early and make sure you say hi to the sound man  before he vanishes off never to be seen again.  You need to make sure you know that everything works OK; you should know where to plug your headphones in and how to switch between the decks on them and how loud you're allowed to take things without blowing up the rig.

Make sure that the monitor's working OK too and find out how to control the level on it (if you can), so you can adjust it if you feel the need. 

If things go wrong
Try not to let if put you off too much - shit happens, and all DJs make serious gaffs from time to time no matter how experienced they are.  If things go very wrong in the middle of a mix; the beats are drifting badly and you have totally lost track of what's wrong - don't worry about cutting your losses and just banging the cross fader across.  Those on the dancefloor will be grateful as dancing to two records that are drifting badly isn't much fun.

Record yourself
If you can record yourself - do so.  It's the same principle as when you're practising - you can listen through after and hear where you went right and where you went wrong and learn from it. Although, do think whether doing this 'll put you off at all as if you think it will, it's best not to bother as you'll be pressured enough anyway.

And...
Hopefully when it's all over, it won't really matter how things actually went - you should feel an incredible buzz from having done it - and quite rightly too!  Playing out really helps you learn what it is you need to focus on in your practising.  Do it and enjoy it.