There are a few ways to welcome someone in Japanese, but the most common or generic phrase you will hear is ようこそ (yōkoso).
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If you are a customer walking into a shop, you would hear いらっしゃいませ (irasshaimase).
welcome (to customers)
Informally, you might hear どうぞ (dōzo) as a kind of welcome or invitation. Generally it is used when permission is given.
here you are / please / by all means
どうぞ、 めしあがって みて ください。
Dōzo, meshiagatte mite kudasai.
Please, try (it).
Yes, please. / (You are) welcome to.
If you want to welcome someone back (normally at home), it's common to use the phrase おかえりなさい (okaerinasai).
welcome back / welcome home
If you want to say "you're welcome" in reply to thanks, you can use the phrase どういたしまして (dōitashimashite) or just a casual いいえ (īe) will do.
you are welcome / don't mention it
no / don't mention it
If you want more lessons on Japanese salutations then I recommend that you check out the following:
じゃあ また！ (Jā mata!)
Sayaka Matsuura: Rocket Japanese
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