Excellent question. I have never liked the word "attack" so I will instead refer to the "entrance" of the note. Basically there are two types of entrances, a "tongued" entrance and a "breath" entrance. Different syllables are used for different styles, but I will just describe the regular style of tonguing used most of the time. You take a breath, set the embouchure, set the tip of the tongue against the tip of the reed, blow (feeling the air pressure behind the tongue), and then pull the tongue off the reed allowing the air to pass as if saying "tu".
That sounds quite complicated, but it is not. To mimic the sensation of tonguing, pretend there is a bit of lint on the tip of your tongue and spit it off. The motion of the tongue and air when doing this is exactly how it feels when you make a tongued entrance on the saxophone. The difference between a tongued entrance and a breath entrance is that you take a breath and go "Hoo" into the mouthpiece instead of "Tu" (or "Too). The important thing to remember about tonguing is that the tongue starts the sound not by hitting the reed but by releasing the reed and the air at the same time.
On longer note values, yes you end the tone by stopping the air. Sing a note on a "La" and then stop the note. Do it the same way on the saxophone. On short notes that are played in a sequence with "tu tu tu tu tu tu tu tu" articulation, the tongue actually stops the previous note as it starts the next note. Sometimes in jazz music the style calls for a short note to be stopped with the tongue like "TUT", "DOT", or "DAUGHT"! However this is generally not done in regular or classical music.
A way to practice that I use with my students is to play long tones while looking at a clock with a second hand. For example, "start on the 12 and hold it till the 6". It makes it more challenging to play with a tuner trying to keep the pitch of the note as steady as possible. Another variation is to start soft on the 12 and crescendo till the 6, or the other way around. You can be creative and come up with lots of variations on your own. Once you have mastered one level, then challenge yourself to make it a bit more difficult and practice that. The possibilities are endless. Good luck. I hope some of these ideas help.