Model Selection in Statistics I have been told not to look at significance level, or not to use forward/backward selection using BIC/AIC for model selection. 
Let's say, I have 100 survey data with 11 variables and I want to see the relation of one of those variables with the rest. I wanted to regress the dependent variable on 10 explanatory variable. But, as I was suggested not to trust significance levels, on what basis do I select a model and confirm that it is indeed the best?
 A: You're right that you should not use significance, or strategies that are based on it (e.g., forward or backward selection, etc.).  
The bigger question is why do you need to select a model at all?  If you want to test a hypothesis about a particular variable, you can do that without any meaningful model selection.  If you want to test a variable while controlling for certain other variables, you can do that too.  You don't need to 'select' a model with certain covariates, just include the variables you were concerned about a-priori.  
On the other hand, if you want to build a model that you will use to make predictions in the future, it is better to focus on what data you will have in the future.  In the predictive context, if you really need to select a model, cross-validation is likely to be your best bet.  
A: Model selection is one of the most difficult task in statistics. There is no silver bullet in finding the best model.
You have to create many models - candidates for champion model.
With your data it should be relatively easy (but no so much instances - a rule of thumb to estimate one variable you need about 30 instances) - in first step create one big model, then few others with backward/forward/stepwise selection and compare them. Both in terms of statistics (AIC, BIC, ...) and interpretation of results.
Don't forget to create transformed variables - thay may improve your model.
