For the exact rules, tap the small "See how to play" text under the big "Add a word" button in Shiritori (the same rules apply to Shiritori Cat, except that one is against the clock, and you find them by tapping the question mark in the bottom left corner after you start a game).
Essentially, it's a word-chain type of game. You find a word that begins with the kana the previous word ends with. You say こと, I say とき (or any other word that starts with と, since it's the kana your word ended with). Bonus points if you overlap with more kana at the end of the word: for example, you say ばけもの, I say ものがたり. If the previous word ends in a compound like きゅ, しょ, じゃ etc., it's enough if you start your word with that ending (ゆっくり, よわさ, やつ, for example).
However, you can't end your word in such a way that no one can find a response to it. Generally, that means you can't use words that end in ん, because there are no words that begin with it. Sure, there are words with な, ね, に, の, ぬ, but Shiritori is played with kana, not sounds. Similarly, you can't end a word in a long-vowel katakana, say かうんたー, because nothing starts with ー.
For kanji shiritori, it's the same, except you need to start your word with the last kanji (one or more) of the last word, regardless of their reading.
Some shiritori games have limitations (use only nouns, use only katakana), and all have bonus points for using words that, on top of the rules above, also include a specific kana: if the bonus kana is こ and the last word is かわいい, you could answer いまだ, but you get extra points if you answer いこくor いとこ, for example.
Now for the hard part: finding the words. I'm afraid I don't have a direct solution, but as you learn more words, it becomes easier. The point of Shiritori is exactly to "activate" that vocabulary that's in your head but just won't come out. :) You can use Renshuu's dictionary to find matching words, but it's best to actually try to learn them, not mechanically copy them into Shiritori just to have played the game.
Sorry, I tried to keep it short. Does that answer your question?
Re: garden: thanks! It's just a heap of random things gathered in time though, other players have much neater and thematic gardens.
