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I am new to German and this site.

I am trying to learn to utter my first phrases in German, and I have learned that the verb is actually placed at the end.

Currently, being a beginner the way I am forming sentences is by saying them in English first (in my head) and converting these words to German later.

So, here is one example:

My friend sent me a card

mein freund hat mir geschickt eine karte.

The above is wrong, at least to Google Translate, as "geschickt" should be place at the end.

My question is very simple. Aside from constructing questions, if I want to build a sentences, should the verb always come at last? If not, then is there a pattern to learn or is there an exception?

Your method won't work. Though both German and English are in the same language family and thus, share a lot of basic vocabulary (with slight modifications), German grammar is much different from English grammar.

My friend sent me a card.

Mein Freund hat mir eine Karte geschickt.

The first thing you notice is English uses the simple past for past events, while German uses Perfekt. That is because tenses in German aren't about the series of events but the intent of speech. So while English has the same auxiliary+participle construction

My friend has sent me a card.

it means a different thing.

In addition, the word order of German sentences is all build on the idea of braces. In English, every item in the sentence has a fairly fixed position. In German in contrary you have a lot of freedom pushing sentence pieces around to get one or another additional emphasis.

To make that work, things belonging together are often split up into two pieces creating an open and close brace. The pieces that are related to those embracing piece are kept inside. And of course, these braces do nest.

Mir hat gerade gestern Abend mein Freund eine Karte geschickt.

This is an alien concept to English speakers. A lot of English speakers consider it counter-intuitive. It makes a lot of sense though as soon as you start thinking in German. You have to embrace it to be able to create beautiful German sentences.

I don't think there is any helpful rule of thumb for this. In a regular declarative sentence, the verb is in the middle:

Ich lerne Deutsch.

In a subordinate clause, it's at the end:

Wir erschrecken über unsere eigenen Sünden, wenn wir sie an anderen erblicken.

Conditional clauses (and questions as you said) have the verb first:

Wär ich ein wilder Falke

There are a lot more cases (types of sentences).