Know when to vote honestly and when to vote deceivingly
With every player having a unique objective, it's crucial to keep your unique objective a secret. This is particularly true in Politburo, where your ability to influence the game result is dependent on the other players' decisions. Let's break down this ability into the two phases of plan and execute.
How to vote in the Plan phase
Most players have an objective that may benefit from any ministry being voted. If you want to maximize Defence, you may still benefit from voting for other plans in order to minimize them. To vote against them risks giving away your objective. On the other hand, it's a shorter path to victory to maximize one ministry compared to minimize two, so sometimes you may have to take the risk. A no vote may also be used to confuse the other players about your objective. In addition, if "your" ministry already has a sufficient level, you may want to vote no to avoid the risk of the other players decreasing the level. Generally, I recommend a yes vote early in the game and a no vote later if the plan is against your objective.
How to vote in the Execute phase
So you have been appointed to the execute phase. Congratulations! Or...? The execute phase is your chance to maximize or minimize the planned ministry depending your objective. However, this isn't without risks - if the vote isn't unanimous, you run the risk of being excluded from further executions or purged in the last execution. Let's look at the executions one by one.
In the first execution, it's usually best to vote according to your objective. If it's generally known that both other players will vote differently, you may possibly want to vote against your objective to keep it secret and avoid a purge in the last execution. If only you know that both other players will vote differently, you may want to vote against your objective to hide your true objective in hope of having another player replaced for the next execution. In most cases, however, it's safest to vote according to your objective to avoid the risk of a unanimous vote against your objective.
In the second execution, there is more room for tactical voting. If you haven't been replaced, you should have a good idea how the others are voting and what vote the general secretary aims for. If your objective coincides with that of the general secretary, you should vote according to that to avoid being replaced in the last exectuion. If not, you should vote so that you avoid a unanimous vote against your objective while still keeping your objective secret and avoiding being replaced. In the best case, your bluff will have yet another player who would vote against your objective replaced.
In the third execution, you should again vote according to your objective. The only exception is if you're sure that your objective will fail anyway, in which case you should avoid a purge (which may strike you).
How about the Purge phase?
If you end up in the purge phase, you should first avoid being purged yourself and second try to purge the right player. This sounds easy but once in the purge phase, there is no way to defend yourself if you're the deviant and the other players know that. Instead, you have to follow the advice from the execute phase to keep your objective secret and, if it fails, prevent the purge phase from taking place. If you're not the deviant, you should have learnt from the previous executions who's likely to have voted against the majority and purge him or her. Which players participated in the execution and what was the result? How did the result change when players were replaced? The process of elimination should help you answer those questions and avoid being purged for not pointing out the deviant.
Finally a few words about minister-specific strategies. Most ministers want to maximize or minimize one ministry and for them, all the advice above apply. The same goes for the the two ministers who want to maximize or minimize all ministries (Bulganin and Khrujhchev). The main difference is that the former may consider avoiding executions that concern another ministry (to minimize the purge risk) while the latter should participate in all executions since every "wrong" vote directly hurts their objective.
The two ministers with influence interests need to be more careful. The minister who wants unanimous votes (Molotov) should participate in all executions and always vote according to the majority. The above advice does help you to find out the likely majority vote. However, you should still "choose" another objective and play according to that. Otherwise, your seemingly irregular play may allow the other players to guess your true objective and stop appointing you to the executions if you're winning.
The minister who wants purges (Zhdanov) is at a greater risk. The best way to cause purges is to vote against the majority but not only may the other players guess your objective and stop appointing you to the executions, they may also purge you. Nevertheless, by following the advice above to vote differently in the different execution rounds, you may be able to cast doubts on other players and have them purge each other instead, just like a true politburo minister!