Your damage on most heroes starts at about 50. The T1 tower damage is 100 to 120. So it kills a range creep in 3 hits and melee creep in 5.
If you try to do one attack it is impossible to get the last hit. There has to be some other dmg on the creep. So you need to replace one of the tower attacks with your attack to get it in range. Do one attack, then count off 4 tower hits for melee creeps or 2 hits for range, then do your 2nd attack and it will almost always get the lasthit. Of course if there is some other damage from heroes/spells/creeps it gets more complicated. But if its just you and the tower it is simple.
Example:
Range creep starts with 300 hp.
Tower hits it for 105, Tower hits it for 110 => range creep has 85 hp
you cannot lasthit this creep
WRONG => once the 2nd tower attack hits you have already missed the chance.
Example:
Range creep starts with 300 hp.
Tower hits for 120, you hit for 50. Tower hits for 107.
Range creep now has 33 hp, you have 1 second to take the last hit before the tower.
RIGHT => still possible to fail but not impossible to succeed.
Until your damage exceeds that of the tower you have to follow this pattern. When you get up to 80 to 90 damage its possible to mix it up. 110 damage + you probably want to just do one attack. If you are static farming, holding the lane position with denies... then you don't have to contest the tower for lasthits at all. But its also easier to gank you.
55 DMG
Ranged creeps: YH+TH+TH+YH
Melee creeps: YH+TH+TH+TH+YH
Catapult: YH+YH+TH+TH+YH
TH towr hit
YH your hit
Practice and timing along with what relentless said
Siege creeps are basically the same thing only the last hit there comes down to the towers damage roll
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Sometimes the towers try be better than you.
Do you guys have some tricks to never lost a last hits under the tower?
Like, if i hit in the same time that tower hit a creep, who get a last hit?