Learn Italian: Non possiamo viaggiare oggi.

In Italian, you don't usually need to say noi (we) because the verb ending already tells you who is doing the action. The form possiamo only ever means "we can", so the "we" is built right in!

Why is viaggiare left in its dictionary form instead of changing to match "we"?

Because it follows a conjugated modal verb. When you use a form of potere (can/to be able to), only the first verb is conjugated. The second verb stays in the infinitive (the dictionary form ending in -are, -ere, or -ire). This works just like English: we say "we can travel", not "we can we travel".

Do I need a connecting word between possiamo and viaggiare?

No. When using a modal verb like potere, the infinitive verb follows it immediately. You just say possiamo viaggiare without any small joining words like a or di in between.

Why is non placed at the very beginning of the sentence?

The negative word non must always go directly before the conjugated verb it is negating (possiamo). Since the subject pronoun noi was dropped, non becomes the first word. If you chose to keep the pronoun, it would be: Noi non possiamo viaggiare oggi.