Your question raises more issues than you probably thought.
With respect to the issue of a relay, then assuming your bike has a 12 volt, negative ground, electrical system, all you need is a generic automotive relay, which looks like this (sometimes called a Bosch relay, regardless of whether it is actually a Bosch unit). Here is an article, which looks accurate at a skim, that describes how relays work, starting with general information and narrowing down on automotive relays specifically (including the standard pinout of 30, 85, 86, and 87).
Before you get that far, you need to consider the output of your generator (I'm guessing your bike has a generator...but it could have an alternator). Cheaper bikes often have undersized generators, and if your energy requirement exceeds your charging capacity, your battery will run flat even while you ride. On a 12 volt system, the stock bulb pulls approximately 3 Amps (35 Watt / 12 Volts). The replacement will pull around 5-5.5 Amps depending on whether you end up using the low or high beam of the H4 bulb (that's an important difference between the bulbs you mention, and I'm sure you saw this already...the H4 has 3 prongs, a common ground in the middle flanked by the positive leads of the high and low beam filaments). If the only powered accessories on the bike are the lights, this could actually be significant (bikes with provisions for other accessories usually have some headroom).
Next is the wiring going to the headlamps. Obviously, go directly from the battery. Make sure you use a thick-enough wire to prevent excessive voltage drop, which will make the light appear dimmer than it should be and overheat the wire. At the amperage of a single 60 Watt bulb, and the distance involved on a motorbike, 18 gauge (American Wire Gauge, or AWG) is the minimum recommended, but I would suggest 16 or even 14 (no such thing as too much wire, so long as the weight penalty is minimal). Make sure you make your connectors weather proof -- that means sealing any solder or crimp joints with marine-grade shrink tubing (which includes adhesive), unless you actually manage to get your hands on a proper, multi-hundred-dollar crimping tool, in which case just crimp and ride. Otherwise your connectors will eventually corrode and fail, and bikes get wet, so this will happen much sooner than you imagine.
Finally, don't expect miracles. Motorcycle lights usually suck, but they don't suck because they are underpowered -- they suck because the optics suck (reflector and lens). In your case, the 35 Watt bulb is also underpowered...but I'm sure the optics are pretty bad as well. I've been riding bikes for about 25 years, and so far I've owned only one with headlights that were good enough to ride with at night with the same level of visibility as a car. Ironically, that was a relatively inexpensive Kawasaki KLR650 (relatively inexpensive by global standards...very cheap by U.S./Canadian standards). I've had to put auxiliary lights on much more expensive and exotic bikes. All those bikes ran 55 or 60 Watt bulbs, but the inefficient reflectors and/or lenses diffused the light excessively, rendering the headlights effectively dim.
Good luck, have fun with the project, and ride safe.