This is not a trivial task and it depends on the lane opponent as well as the role. The only definitive answer is experience.
As an example for an AD Carry you have to look at the base stats, calculate the potential damage and burst as well as the survivability for each level and compare it to other AD Carrys. However, this still gives wrong information since for example Caitlyn with relatively weak burst still has an extremely strong laning phase against many AD Carrys due to her huge range.
As a few rules of thumb:
- Champions with good area of effect Skills are stronger lategame than earlygame since they are more effective in teamfights when they can actually hit multiple targets (ex.: Anivia, Graves)
- Single target burst champions (Assassins) are weak early on, strong in the midgame and fall off lategame when their damage is no longer enough to instantly kill someone (ex.: LeBlanc, Kassadin)
- Champions with a strong long range skill (poking skill) are very useful lategame to soften up opponents prior to engagements but are usually weaker in the laning phase (ex.: Kog'Maw)
- Tanks have a weak early laning phase due to their low damage but become very strong lategame due to their influence on teamfights (ex.: Malphite)
- Champions with crowd control effects (Stuns, snares, blinds, knock ups, knock backs,...) are strong all game long (ex.: Alistar)
- Mobile champions are strong midgame where they can roam but their mobility often comes at the cost of sustained DPS, making them less effective in teamfights (ex.: Ezreal)
- Skill shot based champions are weak in the laning phase but stronger in lategame/teamfights where it's harder to dodge the skill shots
Note that all those rules depend on the actual champion, the opponents, the team composition, the player skill, etc.
As an example i wrote above that Ezreal is less effective in teamfights, which is true only if both teams protect (i.e. peel) for the AD carry, which is often not the case in <1200 ELO teams. If the teams don't peel, the good mobility of Ezreal will be more important than the sustained damage output, giving him an edge in teamfights compared to a stronger, less mobile AD carry.