When it is time to give an answer for the hope within us, keep these things in mind.
1. Reason has its limits
Apart from the work of the Holy Spirit removing blindness and hardhearted-ness, our arguments and rational proofs will not bring anyone into the kingdom. Trust not in your persuasiveness or compelling logic, but in the sovereign God who moves the king's heart like channels of water (Proverbs 21:1). Many people are convinced and brought to Christ less by logical arguments than by receiving compassion, grace and love from followers of the Lord Jesus.
2. The Christian faith is reasonable
At the same time, be diligent to have a reasonable, winsome case for faith. God may use this to bring people to Him, at His pleasure. Christian truth is not confined to reason (witness the doctrine of the Trinity), but the faith is not irrational, either.
The church's evangelism is greatly hindered, because we simply have not thought through ahead of time a 30-60 explanation of our faith, to present in casual conversation. So we say nothing, because we aren't ready.
3. Know your audience
Some people are just looking for a fight, or entertainment, or someone to mock. Don't beat your head against a brick wall. Don't throw pearls before swine. But don't scoff back, either. Always treat people respectfully, even if you are answering a fool according to his folly (Proverbs 26:5). Others genuinely want to know why you would go to all the trouble to go to church, as a for instance. You have more of an opportunity, though probably not time for a 15 minute speech. Do you know your unbelieving coworkers well enough to know their biggest objections to the faith?
4. Know your offense and defense
When you are asked why you do what you do or believe what you do, people often ask with a bit of guarded-ness, acting like they are fine how they are, as a self-defense mechanism, when they are really seeking answers. Be careful not to get overly defensive to a basic question asked with a hint of "you're kind of weird." At that point you are on defense, and that is fine. Assume the burden of proof when others are ignorant of the faith. Be willing to take the time to lay it out for them, if they really want to hear.
These kinds of conversations are two-way streets, usually, not the one-sided speeches we see in the book of Acts. Expect questions and push-back. Sometimes it's time to go on offense. Question their assumptions, which will be flawed somewhere, if they are questioning the faith. Point out the inconsistencies and illogical leaps they are making. It takes as much faith to believe materialism or to be agnostic, as it does to be a Christian. Show where they are asserting and assuming without proof, while they expect you to have a proof for everything. You can be on offense like this without being offensive.
5. Give it time
God usually converts people over an extended process of several conversations with more than one person. Our evangelism is stymied by our ego-centered assumptions that we have to convince, that we have to close the deal now, before they die tomorrow. Shorter conversations, asking to continue it later, takes the pressure off both sides, gives you time to pray, and the Lord will work in their heart in the meantime.