A verb with "te mitai desu" means "want to do something that you haven't done before." "Nihon e itte mitai desu" means "I want to go to Japan someday."
To say what you've been doing, change "masu" at the end of a verb to "te imasu." "Ryokoo-shimasu" (I travel) becomes "ryokoo-shite imasu" (I've been traveling).
To express impressions of what you've experienced, drop the final "i" of an adjective that ends with "i," and add "katta desu." "Tanoshii" becomes "tanoshikatta desu."
To explain a part of your body that ails you, say the part, then the particle "ga," followed by adjectives like "itai," meaning painful, and finally "n desu."
To ask which one among 3 or more things is the best or the most, say "dore ga ichiban," then an adjective like "oishii" (delicious), and finally, "desu ka."
To ask someone to go somewhere with you, say "isshoni" (together), change the verb to the polite negative form, i.e. "ikimasu" to "ikimasen," and finally add "ka."
To explain you've done something before, change a verb to past tense, for example, "yomu" (to read) to "yonda" (to have read), then add "koto arimasu."
To explain that you are having a problem with something, say the name of something, then the particle "ga," and the verb in the negative form followed by "n desu ga."
To explain that you did something you didn't intend to, use the "te" form of a verb, and add "shite shimaimashita." So, "otosu" (to drop) becomes "otoshite shimaimashita."
To ask someone if you can do something, say the verb to indicate your desired action, followed by "koto ga" and "dekimasu," meaning something is possible. Then add "ka."