If you're called in as the second consultant, one tip is to be honest with the other consultant and your client about the state of things without getting too emotional about it.
I wrote a few weeks ago about dealing with the situation when your client calls in another consultant. A number of you asked me to comment on the converse state of affairs -- that is, when you're the one called in second.
First, recognize and utilize the advantage this scenario offers you of foreknowledge. Before you even accept the engagement, you have the opportunity to ask about the working relationships involved. You should find out about the first consultant during your interview for the position. At that point, pursue the question of how you're expected to work with this person. You especially want to know whether they're anticipated to stay on the project or whether they're being phased out of it. If they're staying on, are they losing any responsibilities with your arrival? Are they likely to harbor any resentment towards you?
If you decide to take the engagement, the message you want to get across to everyone is that you're here to solve problems, not to play politics. Even though you may need to rely on the previous consultant more than they need your help, try to offer a helping hand to them whenever you can. Help them to save face in what may be an embarrassing situation as much as you can without being dishonest. Recognize their accomplishments, and tactfully offer suggestions. Try to present your relationship as one of cooperation rather than competition.
The previous consultant may not mirror your helpful attitude. They might drag their feet on sharing information with you, or try to engineer circumstances such that failure appears to be your fault. To avoid these snares, keep communications frequent and honest, especially with the person(s) to whom you both report. But be careful to state the facts dispassionately. If you tell your client enough times that you're waiting on a response from Fred to a specific question, then your client will either light a fire under Fred or suggest some other source for you to use. If, on the other hand, you say "Fred is stonewalling me," then your client might suspect that you're trying to blame Fred for all of your inadequacies. Note the difference between these two remarks -- the second one involves a judgment about Fred's intentions. Let your client draw those conclusions on their own.
If your client asks you to evaluate the previous consultant's performance, answer as honestly and graciously as possible. Stick to facts, and remember that you aren't perfect either. Look for at least one good thing to say about their work. In fact, highlight as many positives as you can. But don't hide any problems from your client. Remember that if you want to keep this client long-term, you need to cultivate a reputation for honesty -- and the best way to do that is to be honest.
As hard as you may work at them, some situations are unworkable. If the previous consultant continually sabotages your efforts and all of your attempts to resolve the situation lead to nought, offer your resignation to your client -- including a thorough, factual, unemotional list of your reasons. If you've been communicating properly, none of these should surprise your client. I would not state "It's either Fred or me" -- you don't want to bully your client. By graciously offering to step aside, you leave the options entirely in your client's hands. Now they can be the hero by saying, "What if I get rid of Fred?"