Universal Quantization is your friend
Clip recording in Ableton Live's Session View is quantized to the Universal Quantization setting and the project's bars/beats position. This works for both starting and stopping clips, which includes recording into them. You do not need to press "stop" precisely, only within the quantization amount before the next unit of time. For example, if you have 1-bar quantization specified, all of your clip triggers will engage on the next bar after the clip is triggered. You can press stop anytime during the last bar of your recording, and the recording will cease when that bar ends. In this way your recorded clips will always begin and end in sync with the project.
So is good timing
Any timing errors you make in your performance will of course be captured as part of the clip - if you play notes early or late, they'll be recorded early or late, even though the clip itself starts and ends on beat, since that's what you played! You can fix this after recording manually or with the quantize feature, and there is a "Record Quantization" setting under the Edit menu which automatically quantizes the clip upon recording, however you do not always necessarily want your performance to be quantized.
Watch out for audio latency
Now, there is one case that is particularly troublesome, and that is when you are playing your MIDI keyboard in time with the other sounds that you hear, and those sounds are delayed by some significant amount because of the inherent latency involved in buffered digital recording. You hear the sounds late, and so your on-time performance is captured with some delay. You can try playing with the output buffer in Live's Audio Preferences to alleviate this, although there is generally a point where too small of a buffer leads to pops, clicks, and errors in the audio stream, so there's a minimum latency you will have to deal with, either by learning to play your keyboard slightly early or by manually selecting all notes in the clip editor and sliding them back in time as a group.