Learn Turkish: Kalemin ucuna bakıyorum. - I am looking at the tip of the pen.

This is an example of consonant mutation. When you add a suffix starting with a vowel to certain words ending in ç, t, k, or p, those hard letters soften. Here, the ç in uç becomes a c when we add the possessive suffix -u to make ucu (its tip).

How exactly do the suffixes on ucuna break down?

It breaks down like this: uç (tip) + -u (possessive suffix for "its") + -n- (a buffer letter) + -a (dative case for "to/at"). Whenever you attach a location or direction suffix (like -a, -da, or -dan) immediately after a 3rd person possessive suffix (like -u or -i), you must use the buffer letter -n- to separate them.

Why is there an -a (dative case) at the very end of ucuna instead of -da (locative case) to mean "at"?

Because of the verb! The verb bakmak (to look) always requires the dative case (-a or -e). In English you say "look at," but Turkish logic is closer to "look to." Since we are directing our gaze towards the tip, we use the directional -a instead of the locative -da.