If you think this question seems straightforward and easy to answer and you'll get five-minute quick tips, I must note that you might be wrong. It would be best to consider several factors before building up a whole strategy; preflop action, players' positions, which determine range and nut advantage, Villain's player type and a few more. Fear not; we'll go around the key factors and highlight some not-so-obvious facts about the ranges so you can notice nuances later while playing.
Range advantage matters
First of all, let's take a look at the preflop action. In many cases, the preflop defender will have a range advantage on low-connected boards (we consider here mainly SRP and 3-bet pots). That's because calling ranges are more merged and tend to outnumber the preflop aggressor in small pocket pairs, suited connectors, gappers and even sometimes low, off-suit hands like 76o or 65o, etc, versus the high pairs, face cards, and so one. As you already know, having a wide range that disconnects with the board is not a good situation range advantage-wise.
There are some exceptions where the preflop aggressor keeps the range advantage. This case typically occurs when the caller (also) lacks low cards. Think about cold calling ranges on the BTN or a BB 3-betting range (and call 3-bet ranges). We strictly mention GTO ranges; You must adjust to Villain's tendencies and table dynamics.
Player types
We've arrived at player types, which also should play a role in how to play your hands on low-connected boards. The better your opponent (or the more likely she takes an aggressive line), the more often you should play passively. Even in some cases, you must consider range checking, especially out of position.
Good players will put you in uncomfortable spots if you missplay your range. The same applies to recreational and aggressive players, who may unintentionally take advantage of you when you over c-bet a board like this.
Position
Naturally, you are allowed to do more betting and generally have more options when you play in position. As you close the action on each street, you'll always have one more piece of information than your opponent does. This allows you to comfortably checkback hands with the intention of pot controlling and still be able to call later street(s).
On the other hand, you almost always have to start with range checking out of position. By doing so, you'll be able to keep your game more simple. Just consider how complicated it is to have a balanced range when you have a betting part plus a checking part of it. Moreover, when you check, you should also have check-call and check-raise hands. Thus, it's a lot more convenient to simplify the game tree and only start by checking.
Case study
Let's look at a very familiar situation, SB 3-bet versus the BTN open, and we arrive at a low-connected board of 
6
5
3.
In our example we look at low-limit GTO ranges;
SB 3-bet vs BTN 2,5bb open
BTN response vs SB 3-bet
blue – fold, red – raise, green – call
We can observe the above-discussed characteristic of the two ranges compared to the flop texture. Now let's take a look at the SB's strategy;
A good rule of thumb is if a GTO solution favours a move close to 80% of the time, we can simplify our decision with very little EV difference. Of course, a solver has a perfectly balanced range, which allows him to choose certain hands that clearly benefit from betting big on the flop. For instance, hands like 88-TT or A6s require a lot of protection, as almost all of the following cards on turns and rivers will be overcards or connecting cards to the board, which allows Villain to outdraw you.
However, looking at our range, most of our hands have virtually zero potential to improve against the top of Villain's range, and the rest of our hands are strong enough to continue by check-calling (such as overpairs). Once again, it will be easier to simplify our game. Just think about the worst-case scenarios had you c-bet your 99 and got raised. Are you happy with the situation?
Conclusion
In today's article, we tried to list the most relevant factors in approaching low-connected boards as the preflop aggressor. It's important to note that in most cases, the defending player has the range advantage in these textures, which also has to be reflected in our strategy. We have to do a lot of checking (even range checking sometimes), depending on our relative position and, naturally Villain's tendencies. You may deviate, too, if you notice deviations in your opponent's game. However, in general, you will need to protect your ranges by checking good bluff catchers (i.e. strong overpairs which may call down three streets) and trap super-strong hands like sets and straights as well.
Hopefully, this article gave you an extra tool on how to battle on low-connected boards! Good luck at the tables!
