Manual Pairing was used for all tournaments before computers became widely available and is quite seviceable for tournaments of 30 people or less.
The following method was described by zinger:
Each player gets an index card assigned to him. Put his name, member #, rank, club ID, and other info near the top. The next line will be round 1, then round 2, etc. When registration is over, you have a little pile of them. Sort this pile by strength, then number them sequentially in the top left corner of the card: these are the player numbers. Post a list with names and pairing numbers so players can find themselves on the crosstable.
|R1||3 (K0.5) W+10||1|
|R3||2 W (K6.5)||(busy)|
Select some form of pairing. Then swap cards here and there, if you want to avoid same-club pairings. Bingo - round 1 is paired. Write in the opponent, color, and handicap on the "round 1" line of each card.
Start a crosstable (Excel if good if you have a laptop, but graph paper works too). First column on the left is the player number. Second column is round 1; third is round 2; etc. The cells need to be big enough to hold several data bits: opponent's player number, White/Black, handicap, result, and running score depending on the tournament scoring. I prefer to have the score as a nice big number, with the other data smaller numbers underneath, but that's up to you.
|1||3 (K0.5) W+10||1||bye||1||2 W (K6.5)||(busy)|
|2||bye||1||3 (K6.5) W-5||1||1 B (H0)||(busy)|
|3||1 (H2) B-10||0||2 (H0) B+5||1||bye||2|
As results are reported, jot them in on each card and the crosstable. Write the player's cumulative score in the top right corner of the card. When all results are in, sort the piles by cumulative score. Now pair the second round, swap cards as appropriate, and repeat.
You will have to use your judgement in pairing, balancing needs of score matching, strength matching, same-club pairings, etc. This is the drawback: if the players complain about the pairings, you can't just say "the computer said so".
When you're done, the crosstable should show every game by round, with result.