How do you make rests and put a note at the end of a bar line?

Please post your MuseScore file and it would be helpful if you would post an image showing what you want it to look like.

To enter rests, select duration, press "0". After entering the rests at the beginning of a measure, you can enter the note at the end. Kind of like pressing "space" a bunch of times to get the cursor to the right hand side of a text editor.

For more on how to enter notes and rests, see Note entry in the Handbook, and/or watch the tutorial videos on the main page of this site.

@Valencys...This is for your particular case: it appears you wish to enter an eighth note (quaver) as the last note in the measure. The score you referenced shows an eighth note for the very first lyric - 'We're' - which is at the end of the measure.
You have already stated: "it should be a 2 beat a 1 beat and a half beat". (Just like in the referenced score.)

So, you would click on the whole rest in an empty measure, then press N to enter note entry mode (the cursor will change). At this point you are at the beginning of the measure, so you really don't want your note at that position, right?
You say you want a 2 beat rest.
OK... press 6 (or click the half note icon on the note duration toolbar) - either way, if you look closely, the half note icon in the toolbar gets highlighted.

Press 0 (zero). This puts the half rest right where you want it - and moves the cursor to the (newly created) half rest which represents the final 2 beats of the measure - beats 3 & 4.
At this point you want a 1 beat rest - so press 5 (or click the quarter note icon on the note duration toolbar) and then enter a quarter rest by again pressing 0 (zero).

At the final beat #4, you say you want a half beat rest, followed by your melody note.
OK... press 4 (or click the eighth note icon), then press 0 (zero) to enter an eighth note rest; and, since the eighth note duration is already selected, just press the letter name of your note, 'A', (the first note of the melody) to enter an actual pitch.
(You can use Ctrl+up arrow or Ctrl+down arrow if MuseScore guesses a different octave from the one you want.)

You see, as Marc mentioned, rests (entering zero) are necessary in music, similar to entering spaces in a text editor. However, unlike a *single* text space, a musical space (rest) can vary in size (duration).

Other things to consider:
I noticed your referenced score is in a standard 'pop song' format - piano/chords/vocals.
For alto sax, if you enter all your notes in 'Concert Pitch', MuseScore will automatically transpose when you turn off 'Concert Pitch'.
See:
http://musescore.org/en/handbook/transposition#Transposing-instruments

Finally, to attach a file - when you create a forum post, click on 'File attachments' (displayed above the 'Save' and 'Preview' buttons). Then browse to your file. Also, attaching a MuseScore file is often the best way forward when you encounter a specific problem.

Regards, and welcome aboard.