As has been more or less already explained, your side deck come into play only between the individual rounds of a duel which are always best of 3. At which time you can choose to switch cards in your deck with those in your side deck. Yes you can look at your deck and side and pick which ones, but you must end up with 15 cards still in your side deck afterwards before starting the next round.
Side decks are extremely useful as there are a lot of decks that you really need certain types of cards to get around, take a Burn deck for example - these decks nearly always contain a lot of spell and trap cards to stop you from attacking so that they can burn you down with effect cards as oppose to attacking with monsters, so when facing a burn deck it's a good idea to side in cards that destroy spells and traps such as Mobius The Frost Monarch, Dust Tornadoes, Heavy Storm (Although storm is a card that should be in your main deck all the time) etc etc.
But some players use their side decks to completely change their deck theme between rounds, making it impossible for their opponent to predict what cards they should side in, for example.
If you were playing me in a duel and I was maining Royal Decree- a trap which negates all other trap cards on the field, whilst you had a deck with lots of trap cards, after round one your instinct may be to switch your trap cards out of your main deck and side in a load of other random stuff, but at the same time I may side out my Decrees meaning that in the next round you would have sided our your traps for no reason, whilst I 1: Don't have to worry about your traps 2: Don't have 1/2/3 decrees still in my deck making them dead draws against a deck with little or no traps.
But then again, players could double bluff and whilst I am siding out my decrees, you would actually keep your traps and just make it look like your siding them out (see shadowballing at the bottom of the page) so I would have mistakenly sided out my decrees.
Siding is as dangerous as it is useful as one wrong sided card could lose you the game, an example of this was UK Nationals 05 in the top 8 match between James Pennicott and and 05 nats champ Adam Kruzinsci, James was playing a Horus deck, and in round 3 sided out his Horus LV8 in fear of drawing it at the wrong time and costing him the duel, but as gthe match went on James got his LV6 out and had the oppurtunity to level it up which would have won him the game in aabout 1 turn, but as he has sided it out he couldn't and Adam pulled back.
Shadowballing - A technique used by a lot of Pro duelests where between round you shuffle all 15 cards from your side, into your main deck and then remove 15, this way your opponent has no wal of telling how many cards you have sided wether it be none or 15, even if they stare at you while siding lol.
Hope this has helped.