A 95% interval is roughly the estimate plus or minus 1.96 standard errors, under normality.
The trap, and it is a real one. A 95% interval does not mean there is a 95% probability the parameter lies in this interval. The parameter is fixed; the interval is random. The 95% refers to the long-run coverage of the procedure, not to your particular result.
The statement people want - probability the parameter is in the range - is a Bayesian credible interval, which requires a prior.