1. Short Form:
Al– : is the
Aleekum: on you
2. Long Form: [complete formal form]
Alsalaamu aleekum wa rahmatu allah wa barakaatu
It can be translated to: Hello, may the peace, mercy and blessings of God be with you. [This is not exactly a literal translation but it certainly explains the meaning perfectly.]
To reply: Wa aleekum alsalaam wa rahmat allah wa barakaatu.
[The same meaning as the previous one.]
In Egypt we use a more informal language to communicate in our daily life, while we use a formal language in writing mostly.
Hello, we just say Ahlan.
And to reply you can just say Ahlan.
Now, to say Hello and Welcome! just say Ahlan wa Sahlan!