Duelist Kingdom had a simplified card play and battle system. It had some major differences to the real life game. These rules were seemingly made up as the creators went along, with some cards having very specific rules and exceptions that were not always consistently applied.
Each Attribute or Type had a strength and weakness against another. A superior monster will always either automatically destroy an inferior monster or lower its ATK by a certain amount (usually by 360 or returning the inferior monster's ATK to its original one).
If a monster was played in its favored terrain, it would receive a 30% increase in its ATK and DEF points.
All Class A Toon Monsters seen in the first season were not able to attack directly but were immune to attacks from non-Toon monsters unless restrained (or prevented from attacking), and had to be Summoned via sacrificing its normal counterpart via the effect of "Toon World".
If a certain Trap Card is Set, it automatically activates if it meets its requirement for activation. The controller has no control when this happens.
Although it is implied that there are no direct attacks, direct attacks never occur because players Summon monsters in order to protect their Life Points (as seen in the very first episode when Yugi "must" Summon Exodia or all 3 of Kaiba's "Blue-Eyes White Dragon" will attack and finish off Yugi's Life Points).
Toon monsters were much more accurate to the current TCG rules in this season, but they were still immune to attacks from non-Toon monsters.
It seems that if you're participating in Tag-Team Duel, you can still activate cards that affect your partner even after you officially lost the Duel. This was proven when Yugi and Seto faced Dartz because Seto activated "Wish of Final Effort" after his Life Points hit 0.