Make sure you have read the legal bit on my home page.
In English, a transitive verb has a direct object. You did check that you know what a direct object is, didn't you?
In Japanese, the term is "other-verb" - the subject does the action to something or someone else. It amounts to the same thing.
The direct object particle is wo (pronounced o).
mahoutsukaisamahajuubakuwotatarisoudesu. "The wizard seems to be casting a binding spell."
That was easy, wasn't it? The trick here is that some verbs which are transitive in English are intransitive in Japanese, and vice versa. For example, aruku ("to walk") is transitive: the direct object is the thing being walked on. And au ("to meet") is intransitive: the person being met is an indirect object (use ni). There's no rule - these exceptions have to be learnt one by one.
Since the particles make clear which is the direct object and which the indirect, the order isn't important. For example, the following two sentences mean the same:
saburinasanhasupu-ndegohanwotabemashita. "Sabrina ate rice with a spoon."
saburinasanhagohanwosupu-ndetabemashita. "Sabrina ate rice with a spoon."
Present/future tense and negatives are straightforward. So is eating Japanese rice with chopsticks.
Japanese has a large number of verbs which express doing things. It's difficult to remember them all. Fortunately, there's an alternative. THINGsuru or THINGwosuru is almost always acceptable for doing something.
For example, the following two sentences mean much the same:
saburinasanhaodorimashita. "Sabrina danced."
saburinasanhadansuwoshimashita. "Sabrina danced."
The particle wo comes and goes; it's usually OK to include it (THING is what was done, so it's the direct object) and it's usually also OK to omit it (THING is part of a compound verb). The following two examples are identical in meaning.
watashihabenkyowoshiteimasu. "I am studying". benkyo is "study" as a noun - "I am doing study".
watashihabenkyoshiteimasu. "I am studying". benkyosuru is "study" as a verb.
If THING itself has a direct object, it's necessary to omit the second wo (a sentence cannot have two direct objects).
watashihanihongowobenkyoshiteimasu. "I am studying Japanese". nihongo is "Japanese". nihongo is the direct object of benkyosuru.
watashihanihongonobenkyowoshiteimasu. "I am studying Japanese". This is OK too - nihongonobenkyo "the study of Japanese" is the direct object of suru.
The THINGsuru and THINGwosuru patterns are particularly useful for actions which are loan words, since loan words are almost always nouns.
saburinasanhaberi-dansuwoshimashita. "Sabrina did a belly-dance."
saburinasanhago-go-dansuwoshimashita. "Sabrina did a gogo-dance."
The THINGsuru construction is often used for mental states. For example:
saburinasanhatouwakushimashita. "Sabrina was confused." touwaku is "confusion" as a mental state.
saburinasanhabi,kurishimashita. "Sabrina was surprised" or "Sabrina was startled". bi,kuri is "surprise" as a mental state.
For many, many more transitive verbs, see the Can of Worms, a list of transitive and intransitive verbs in Japanese.