Almaty and Karakol are closer to each other than either is to their own capital cities, which surprises a lot of travelers routing through Central Asia. The most direct crossing for this route is Kegen–Kyzyl-Suu, on the northeastern side of Issyk-Kul.
Border processing itself is usually straightforward for most passport holders, typically 30-60 minutes depending on traffic, but the approach roads on both sides are slower than the map distance suggests — budget a full day for Almaty to Karakol door to door.
Check current visa requirements for Kyrgyzstan before you travel, since they vary by nationality and do change. Shared taxis run this route from both sides, or you can arrange a private transfer — either way, this isn't a crossing to attempt late in the day, since facilities on the Kyrgyz side thin out after dark.