"You are Alasdair."
Translation:Is tusa Alasdair.
This may help a little more in a different way to understand, although the explanation before is very defined and precise (!):
When it is a definition (equal / =) use the verb is: Is mise Alasdair (by definition, not changeable without biggest administrative efforts ;-))
Use the verb bi, specifically tha, bha, bidh etc. when you characterize somebody/something: Tha Iain brònach (this moment, may change within few minutes or days, etc.) Bha am peann air bòrd (obviously the pen was on a table this situation, but now...?)
I think with this hint, the usage of is and bi may work for most of the time...
The short, but not very helpful answer is that there are two verbs 'to be' in Gaelic, and you just have to learn to use th right one.
The longer answer actually covers quite a few different points of grammar.
The sa in tusa
This is an emphatic particle. It is conventional, but not strictly necessary, to use it when saying who someone is.
The missing h in tu
Thu loses its h after is, bu and other verb forms that end in -s or -dh. This is discussed further on this question.
Is instead of tha
Several languages have two verbs 'to be'. One (called the copula) is used where you could use an equals sign (as here)
You = Alasdair, or
Alasdair = you
They usually make sense if you reverse them. On the other hand, the substantive verb is used to say something about you
You are singing (verbal noun)
You are clever (adjective)
You are in Scotland (prepositional phrase)
These are characterized by not being reversible and not making sense with an equals sign. I think (someone please correct me if I am wrong) that you can only use tha if followed by one of these three things.
There are, however, some other uses of is that you have met or will meet, but they are taught separately.
Several languages have this pair of words 'to be'. Compare mae and yw/ydy in Welsh or this article on Spanish in Wikipedia (where they seem to call both verbs 'copulas'). The rules for which verb to use vary from language to language and cause endless confusion for learners. D