Restringing should be the easiest thing and you should learn to do it cause strings break quit often or need replacing after a while. With some practice you can do it in a few minutes, which will beat going to a shop every time.
Just remove the pieces of the broken string. With me they tend to break near the bridge so the ball end sometimes remains in the floating bridge of a tremolo. Put a new string through the correct holes, fasten them to the tuners and tune away using the tuning device I assume you have. When its in tune pull on the string so it starts to get out of tune again. New strings can have some slack so you need to do this a few times until you notice it no longer gets out of tune. Then start tuning all strings since a strat has a floating bridge and the loss of tension of one string broken means they all will get out of tune. Then you should be set.
Remember that you need to replace old strings, even if they haven't broken, cause older strings tend to lose tone and could get contaminated with rust and sweat and grease from your fingers. Most professional guitarists change strings for every show. Edge is rumored to have his guitars restrung every time he's finished playing them after a song. No need to go through those extremes. Once every few months will serve you well. Remember that because you have a strat with a floating bridge its better to change strings one at a time then to remove them all and then restring them.
Maybe others have some useful tips.