Pairing can get too scientific.  We have tried to give the basics here, but as long as you follow the 1-4 list below, you can't go far wrong.  

In adult chess, the pairing rules are necessarily complicated and a more detailed version of these.  However, we give you principles of pairing in order of importance and suggests as to how to go about doing them.
1   You cannot pair a player against another more than once in the same tournament.
2   You should pair players against others on (or as close to) the same score as them - starting from the highest score and working down.
3   You should seek to equalise the number of blacks and whites were possible 
      (ie. if they have had 2 blacks and 1 white so far, they ideally need white)
4   You should seek to alternate the numbers of blacks and whites where possible.
      (ie. if they had black last time, you hope to give them white this time)
There is a program you can download for around 20 called Swissperfect and once you have it registered, you can use it forever.  Go to www.swissperfect.com for the links - contact CCF if you need any advice.  Using this program, you can run the whole tournament (and any others you want) and it will be provide you with a cross table that you can send to CCF at the end by email.  If you request, one of the arbiters from CCF will be pleased to assist you to understand how to use the program.  Call 020 8645 0302 or email us to request assistance.
(we are going to presume a field of 16 when giving examples but any number can work)
We strongly recommend you use the pairing cards to do this.  A sheet will describe how to fill them in.  
* Unless you want to do a random draw (which is fine), work out the players into descending order of strength and indicate their order of strength using the square in the top right hand corner (this can all be done with a little guesswork if you wish but should be reasonably accurate if possible).  
* Toss a coin.  If the coin comes down heads, give the top player white.  If the coin comes down tails, give them black.  
*  If player 1 has white then the pairings will be (with the "white" player named first): 1v9, 10v2, 3v11, 12v4, 5v13, 14v6, 7v15, 16v8.  If the top player gets black, then you merely reverse the colours with the same opponents.  If there is an odd number of players (someone might be ill or missing - or maybe you do have an odd number anyway), give the "middle" ranked player the bye and award them the full 3 points.
ROUND 2 (follow this principle in subsequent rounds as well):
* Place the pairing cards in piles of score.  All those who won their 1st game will be on 3 points.  All those who drew will be on 2 and all those who lost will be on 1.  Of course, you might have some who didn't play so defaulted and are therefore on 0. 
* Take the cards for those on the highest score group and split them into those seeking black and those seeking white (those that played black in the first round are obviously seeking white if possible).  
*  Follow the principle of the instructions in round 1, except that you now do NOT need to toss a coin for colours, etc.  Basically, the top half of the players on ranking play the bottom half as before.
NOTE: You might have to balance piles of colours by moving some of the lower rated players across as you cannot mix the score groups just to balance colours.  Also, you might have a total odd number in a particular score group.  If this happens, one of the players must be passed down to the next score group (2) to be paired with them.  This in turn can cause another odd number at the bottom of that score group requiring someone else to move down a score group, but that is the way it works as you work from the top down.  When this happens, it is called a float.  Normally you try and balance floats as much as possible during the whole event (so if someone has upfloated, they are the first choice to downfloat in a future round - and vice-versa).  If you have an off number in the tournament, somebody from the bottom score group is given a bye (nobody may get more than one such bye in an event).