Is there any algorithm for 3SAT problem that is fast and relatively easy to implement?
If you're determined not to use the standard deterministic algorithm, the usual alternative is what's known as local search or stochastic search.  The basic idea is that you start with a random bit pattern as a variable assignment, observe what's wrong with it in terms of unsatisfied clauses and try to improve it by flipping one or more variable assignments.  Observe how this new assignment fails, try to improve it, and repeat.
Local search typically outperforms deterministic search for satisfiable random SAT instances, but performs poorly on more structured instances.  It also offers no way to prove unsatisfiability unless some proof system is layered atop it.
There are various local search algorithms on offer, from Uwe Schöning's scheme to PPSZ and its variants.  None of them outperform DPLL-based solvers on all instances.